\relax \catcode`Ÿ\active \select@language{greek} \@writefile{toc}{\select@language{greek}} \@writefile{lof}{\select@language{greek}} \@writefile{lot}{\select@language{greek}} \newlabel{Perieq'omena}{{}{7}} \@writefile{toc}{\contentsline {chapter}{\numberline {1}Arijmhtik'ec M'ejodoi}{9}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {1.1}Eisagwg'h}{9}} \newlabel{sec:eisa}{{1.1}{9}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.1}Genik'h Strathgik'h}{10}} \@writefile{toc}{\contentsline {section}{\numberline {1.2}Prosegg'iseic stouc Episthmoniko'uc Upologismo'uc}{11}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.1}Phg'ec Pros'eggishc}{11}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.2}Sf'almata Dedom'enwn kai Sf'almata Upologism'wn}{13}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.3}Sf'alma Apokop'hc kai Sf'alma Strogg'uleushc}{13}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.4}Ap'oluto kai Sqetik'o Sf'alma}{14}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.5}Euaisjhs'ia kai Kat'astash}{15}} \@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces Sqhmatik'o di'agramma thc proc ta p'isw an'alushc sfalm'atwn.}}{17}} \newlabel{back}{{1.1}{17}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.6}Proc ta P'isw An'alush Sfalm'atwn}{17}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.7}Eust'ajeia kai Akr'ibeia}{19}} \@writefile{toc}{\contentsline {section}{\numberline {1.3}Arijmhtik'h Upologist'h}{19}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}Arijmo'i Kinht'hc Upodiastol'hc}{19}} \@writefile{lot}{\contentsline {table}{\numberline {1.1}{\ignorespaces Par'ametroi merik'wn tupik'wn susthm'atwn kinht'hc upodiastol'hc}}{21}} \newlabel{tbl:val}{{1.1}{21}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.2}Kanonikopo'ihsh}{21}} \@writefile{lof}{\contentsline {figure}{\numberline {1.2}{\ignorespaces foo}}{22}} \newlabel{fig:1.2}{{1.2}{22}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.3}Idi'othtec Susthm'atwn Arijm'wn Kinht'hc Upodiastol'hc}{22}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.4}Strogg'uleush}{23}} \@writefile{lot}{\contentsline {table}{\numberline {1.2}{\ignorespaces Kan'onec Strogg'uleushc.}}{24}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.5}Akr'ibeia Mhqan'hc}{24}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.6}Upokanoniko'i kai Stadiak'h Upoekqe'ilish.}{25}} \@writefile{lof}{\contentsline {figure}{\numberline {1.3}{\ignorespaces Par'adeigma}}{26}} \newlabel{fig:1.3}{{1.3}{26}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.7}Exairetik'ec Tim'ec}{26}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.8}Arijmhtik'h Kinht'hc Upodiastol'hc}{27}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.9}Ap'wleia shmantik'wn yhf'iwn}{29}} \@writefile{lot}{\contentsline {table}{\numberline {1.3}{\ignorespaces Upologism'enec tim'ec gia thn olik'h en'ergeia tou at'omou tou hl'iou}}{31}} \newlabel{tbl:1.2}{{1.3}{31}} \@writefile{lof}{\contentsline {figure}{\numberline {1.4}{\ignorespaces Sf'alma sthn pros'eggish me peperasm'enec diafor'ec wc sun'arthsh thc param'etrou diakritopo'ihshc.}}{33}} \newlabel{fig:1.4}{{1.4}{33}} \@writefile{toc}{\contentsline {section}{\numberline {1.4}Majhmatik'o Logismik'o}{35}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.1}Biblioj'hkec Majhmatiko'u Logismiko'u}{36}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.2}Perib'allon Episthmonik'wn Upologism'wn}{37}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.3}Praktik'ec Sumboul'ec gia to Logismik'o}{39}} \@writefile{toc}{\contentsline {section}{\numberline {1.5}Istorik'ec Shmei'wseic kai Perait'erw An'agnwsh}{42}} \newlabel{kef1}{{1.5}{57}} \@writefile{toc}{\contentsline {chapter}{\numberline {2}Sust'hmata Grammik'wn Exis'wsewn}{59}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {2.1}Gramik'a sust'hmata}{59}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1.1}Idi'azontec kai Mh-idi'azontec P'inakec}{60}} \@writefile{toc}{\contentsline {section}{\numberline {2.2}Ep'ilush Grammik'wn Susthm'atwn}{61}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}Trigwnik'a Grammik'a Sust'hmata}{63}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.2}Stoiqei'wdeic P'inakec Apaloif'hc}{64}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.3}Apaloif'h $Gauss$ kai $LU$ Paragontopo'ihsh.}{66}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.4}Od'hghsh}{69}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.5}Ulopo'ihsh thc Apaloif'hc $Gauss$}{75}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.6}Poluplok'othta thc Ep'ilushc Grammik'wn Susthm'atwn}{77}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.7}H Apaloif'h $Gauss-Jordan$}{78}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.8}Ep'ilush Tropopoihm'enwn Problhm'atwn}{80}} \@writefile{toc}{\contentsline {section}{\numberline {2.3}N'ormec kai Arijmo'i Kat'astashc}{83}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3.1}N'ormec Dianusm'atwn}{83}} \@writefile{lof}{\contentsline {figure}{\numberline {2.1}{\ignorespaces H monadia'ia sfa'ira se poik'ilec n'ormec dianusm'atwn}}{84}} \newlabel{fig2.1}{{2.1}{84}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3.2}N'ormec Pin'akwn}{85}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3.3}De'ikthc (Arijm'oc) Kat'astashc en'oc P'inaka}{86}} \@writefile{toc}{\contentsline {section}{\numberline {2.4}Akr'ibeia L'usewn}{88}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.1}Up'oloipo miac L'ushc}{88}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.2}Ekt'imhsh Akr'ibeiac}{90}} \@writefile{lof}{\contentsline {figure}{\numberline {2.2}{\ignorespaces Kal'hc kat'astashc kai kak'hc kat'astashc grammik'a sust'hmata.}}{91}} \newlabel{fig:2.2}{{2.2}{91}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.3}Belt'iwsh thc Akr'ibeiac}{92}} \newlabel{kef2}{{2.4.3}{94}} \@writefile{toc}{\contentsline {chapter}{\numberline {3}Grammik'a El'aqista Tetr'agwna}{95}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {3.1}Prosarmog'h Dedom'enwn}{95}} \@writefile{toc}{\contentsline {section}{\numberline {3.2}Grammik'a el'aqista tetr'agwna}{96}} \@writefile{lof}{\contentsline {figure}{\numberline {3.1}{\ignorespaces Elax}}{97}} \newlabel{fig:}{{3.1}{97}} \@writefile{toc}{\contentsline {section}{\numberline {3.3}M'ejodoc kaj'etwn}{97}} \newlabel{sec:normal}{{3.3}{97}} \@writefile{lof}{\contentsline {figure}{\numberline {3.2}{\ignorespaces Gewmetrik'h perigraf'h}}{98}} \newlabel{fig:???}{{3.2}{98}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.3.1}Orjogwni'othta}{98}} \newlabel{ssec:normal:ort}{{3.3.1}{98}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.3.2}M'ejodoi}{98}} \newlabel{ssec:normal:normal}{{3.3.2}{98}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.3.3}Au }{99}} \newlabel{ssec:normal:au}{{3.3.3}{99}} \@writefile{toc}{\contentsline {section}{\numberline {3.4}M'ejodoi Orjogwnopo'ihshc}{99}} \newlabel{sec:ortho}{{3.4}{99}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4.1}Trigwnik'a}{99}} \newlabel{ssec:ortho:tri}{{3.4.1}{99}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4.2}Orjog'wnioi metasqhmatismo'i}{100}} \newlabel{ssec:ortho:met}{{3.4.2}{100}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4.3}Paragwntopoihsh QR }{100}} \newlabel{ssec:ortho:qr}{{3.4.3}{100}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4.4} ? }{100}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4.5}Peristrof'h $Givens$}{104}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4.6}Orjogwniopo'ihsh $Graham-Schmidt$}{108}} \@writefile{lof}{\contentsline {figure}{\numberline {3.3}{\ignorespaces 'Ena ap'o ta b'hmata thc orjogwniopo'ihshc $Gram\ -\ Schmidt$}}{109}} \newlabel{fig3.3}{{3.3}{109}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4.7}'Elleiyh diast'asewn.}{112}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4.8}Od'hghsh sthl'wn}{113}} \@writefile{toc}{\contentsline {section}{\numberline {3.5}S'ugkrish Mej'odwn}{114}} \@writefile{toc}{\contentsline {section}{\numberline {3.6}Logismik'o gia Grammik'a Probl'hmata Elaq'istwn Tetrag'wnwn}{114}} \@writefile{lot}{\contentsline {table}{\numberline {3.1}{\ignorespaces Logismik'o gia grammik'a probl'hmata elaq'istwn tetrag'wnwn}}{115}} \newlabel{}{{3.1}{115}} \@writefile{toc}{\contentsline {section}{\numberline {3.7}Istorik'ec shmei'wseic kai epipr'osjeth mel'eth}{116}} \newlabel{kef3}{{3.7}{127}} \@writefile{toc}{\contentsline {chapter}{\numberline {4}Idiotim'ec kai Idi'azousec Tim'ec}{129}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {4.1}IDIOTIMES KAI IDIODIANUSMATA}{129}} \newlabel{sec:gram}{{4.1}{129}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.1.1}Qarakthristik'o Polu'wnumo}{129}} \newlabel{ssec:gram:ant}{{4.1.1}{129}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.1.2}Idi'othtec twn Problhm'atwn Idiotim'wn}{130}} \newlabel{ssec:gram:ant}{{4.1.2}{130}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.1.3}Metasqhmatismo'i Omoi'othtac}{130}} \newlabel{ssec:gram:ant}{{4.1.3}{130}} \@writefile{toc}{\contentsline {section}{\numberline {4.2}MEJODOI UPOLOGISMOU OLWN TWN IDIOTIMWN}{131}} \newlabel{sec:gram}{{4.2}{131}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}Qarakthristik'a Polu'wnuma}{131}} \newlabel{ssec:gram:ant}{{4.2.1}{131}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}H M'ejodoc $Jacobi$ gia Summetriko'uc P'inakec}{131}} \newlabel{ssec:gram:ant}{{4.2.2}{131}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2.3}Epanal'hyeic $QR$}{132}} \newlabel{ssec:gram:ant}{{4.2.3}{132}} \@writefile{toc}{\contentsline {section}{\numberline {4.3}MEJODOI UPOLOGISMOU SUGKEKRIMENWN IDIOTIMWN}{132}} \newlabel{sec:gram}{{4.3}{132}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.1}M'ejodoc Dunamiko'u}{132}} \newlabel{ssec:gram:ant}{{4.3.1}{132}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.2}Normalization}{133}} \newlabel{ssec:gram:ant}{{4.3.2}{133}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.3}Gewmetrik'h Je'wrhsh}{133}} \newlabel{ssec:gram:ant}{{4.3.3}{133}} \@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces Gew}}{134}} \newlabel{fig:}{{4.1}{134}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.4}Metatwp'iseic}{134}} \newlabel{ssec:gram:ant}{{4.3.4}{134}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.5}Deflaction}{134}} \newlabel{ssec:gram:ant}{{4.3.5}{134}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.6}Ant'istrofec Epanal'hyeic}{134}} \newlabel{ssec:gram:ant}{{4.3.6}{134}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.7}Up'oloipo tou $Rayleigh$}{135}} \newlabel{ssec:gram:ant}{{4.3.7}{135}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.8}Epanal'hyeic $Rayleigh$}{135}} \newlabel{ssec:gram:ant}{{4.3.8}{135}} \@writefile{lof}{\contentsline {figure}{\numberline {4.2}{\ignorespaces S'ugklish twn Tim'wn $Ritz$}}{136}} \newlabel{fig:ritz}{{4.2}{136}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.9}H M'ejodoc tou $Lanczos$}{136}} \newlabel{ssec:gram:ant}{{4.3.9}{136}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.10}M'ejodoi Temaqismo'u tou F'asmatoc gia Summetriko'uc P'inakec}{136}} \newlabel{ssec:gram:ant}{{4.3.10}{136}} \@writefile{toc}{\contentsline {section}{\numberline {4.4}GENIKEUMENA PROBLHMA IDIOTIMWN}{136}} \newlabel{sec:gram}{{4.4}{136}} \@writefile{toc}{\contentsline {section}{\numberline {4.5}IDIAZOUSES TIMES}{136}} \newlabel{sec:gram}{{4.5}{136}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5.1}Paragontopo'ihsh Idi'azouswn Tim'wn}{136}} \newlabel{ssec:gram:ant}{{4.5.1}{136}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5.2}Efarmog'ec thc $SVD$}{137}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5.3}LOGISMIKO GIA IDIOTIMES}{139}} \@writefile{lot}{\contentsline {table}{\numberline {4.1}{\ignorespaces Logismik'o gia tupik'a, apl'a probl'hmata upologismo'u idiotim'wn}}{140}} \newlabel{tbl:4.3}{{4.1}{140}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5.4}ISTORIKES SHMEIWSEIS KAI EPIPROSJETO DIABASMA}{141}} \newlabel{kef4}{{4.5.4}{158}} \@writefile{toc}{\contentsline {chapter}{\numberline {5}Mh-grammik'ec Exis'wseic}{159}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {5.1}MH GRAMMIKES EXISWSEIS}{159}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.1.1}L'useic Mh Grammik'wn Exis'wsewn}{160}} \@writefile{lof}{\contentsline {figure}{\numberline {5.1}{\ignorespaces Mh grammik'ec exis'wseic pou 'eqoun m'ia pollapl'h r'iza.}}{161}} \newlabel{fig:5.1}{{5.1}{161}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.1.2}RUJMOS SUGKLISHS EPANALHPTIKWN MEJODWN}{161}} \@writefile{toc}{\contentsline {section}{\numberline {5.2}MH GRAMMIKES EXISWSEIS SE MIA DIASTASH}{162}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.1}MEJODOS DIQOTOMHSHS}{162}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.2}Epanal'hyeic stajero'u shme'iou}{164}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.3}MEJODOS TOU NEUTONOS.}{166}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.4}M'ejodoc thc t'emnousac}{168}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.5}ANTISTROFH PAREMBOLH}{170}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.6}Grammik'h klasmatik'h parembol'h}{171}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.7}$Safeguarded$ m'ejodoc}{172}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.8}Mhdenik'a twn poluwn'umwn}{173}} \@writefile{toc}{\contentsline {section}{\numberline {5.3}SUSTHMATA MH GRAMMIKWN EXISWSEWN}{174}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.3.1}Epan'alhyh stajero'u shme'iou}{174}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.3.2}H MEJODOS TOU NEUTONA}{175}} \newlabel{kef5}{{5.3.2}{175}} \@writefile{toc}{\contentsline {chapter}{\numberline {6}Beltistopoi'hsh}{177}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {subsection}{\numberline {6.0.3}Sq'esh me Mh Grammik'a Probl'hmata}{177}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.0.4}Akr'ibeia twn L'usewn}{178}} \@writefile{toc}{\contentsline {section}{\numberline {6.1}BELTISTOPOIHSH SE MIA DIASTASH}{179}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.1.1}'Ereuna gia Qrus'h Tom'h}{179}} \@writefile{lof}{\contentsline {figure}{\numberline {6.1}{\ignorespaces Pr'wth epan'alhyh thc 'ereunac qrus'hc tom'hc gia to pr'oblhma tou parade'igmatoc}}{182}} \newlabel{fig:6.2}{{6.1}{182}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.1.2}Diadoqik'h Parembol'h Parabol'wn}{182}} \@writefile{lof}{\contentsline {figure}{\numberline {6.2}{\ignorespaces Diadoqik'ec parabolik'ec epanal'hyeic gia thn elaqistopo'ihsh m'iacsun'arthshc}}{183}} \@writefile{lof}{\contentsline {figure}{\numberline {6.3}{\ignorespaces H pr'wth ap'o tic diadoqik'ec parabolik'ec epanal'hyeic tou probl'hmatoc tou parade'igmatoc}}{183}} \newlabel{fig6.4}{{6.3}{183}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.1.3}M'ejodoc $Newton$}{183}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.1.4}M'ejodoi asfale'iac}{184}} \@writefile{toc}{\contentsline {section}{\numberline {6.2}POLUDIASTATH FUSIKH BELTISTOPOIHSH}{184}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2.1}mesec M'ejodoi 'Ereunac}{184}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2.2}H M'ejodoc thc M'egisthc Arnhtik'hc Kl'ishc}{185}} \@writefile{lof}{\contentsline {figure}{\numberline {6.4}{\ignorespaces }}{186}} \newlabel{fig6.5}{{6.4}{186}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2.3}H M'ejodoc $Newton$}{186}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2.4}M'ejodoi $Quasi-Newton$}{189}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2.5}M'ejodoi Enhm'erwshc twn $secant$}{190}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2.6}M'ejodoc Koin'wn Qarakthristik'wn twn Kl'isewn}{191}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2.7}Apokomm'enec M'ejodoi $Newton$}{193}} \newlabel{kef6}{{6.2.7}{194}} \@writefile{toc}{\contentsline {chapter}{\numberline {7}Parembol'h}{195}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {7.1}PAREMBOLH}{195}} \@writefile{toc}{\contentsline {subsection}{\numberline {7.1.1}O Skop'oc thc Parembol'hc}{196}} \@writefile{toc}{\contentsline {subsection}{\numberline {7.1.2}Parembol'h enant'ion Pros'eggishc}{196}} \@writefile{toc}{\contentsline {subsection}{\numberline {7.1.3}Epilog'h thc Paremb'alousac}{196}} \newlabel{kef7}{{7.1.3}{196}} \@writefile{toc}{\contentsline {chapter}{\numberline {8}Arijmhtik'h Olokl'hrwsh kai Diaf'orish}{197}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {8.1}ARIJMHTIKH OLOKLHRWSH}{197}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.1.1}Kan'onec Olokl'hrwshc}{197}} \newlabel{kef8}{{8.1.1}{198}} \@writefile{toc}{\contentsline {chapter}{\numberline {9}Probl'hmata Arqik'wn Tim'wn Sun'hjwn Diaforik'wn Exis'wsewn}{199}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {9.1}SUNHJHS DIAFORIKES EXISWSEIS}{199}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.1.1}Probl'hmata Arqik'wn Tim'wn}{200}} \@writefile{lof}{\contentsline {figure}{\numberline {9.1}{\ignorespaces Grafik'h par'astash merik'wn mel'wn thc oikog'eneiac twn l'usewn thc SDE $y' = y$.}}{201}} \newlabel{fig9.1}{{9.1}{201}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.1.2}SDE Uyhl'oterhc T'axhc}{201}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.1.3}Eustaje'ic kai Astaje'ic SDE}{202}} \@writefile{toc}{\contentsline {section}{\numberline {9.2}ARIJMHTIKH LUSH TWN ODES}{205}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.2.1}H M'ejodoc $Euler$}{205}} \@writefile{toc}{\contentsline {section}{\numberline {9.3}AKRIBEIA KAI STAJEROTHTA}{207}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.3.1}Bajm'oc Akr'ibeiac}{207}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.3.2}Stajer'othta m'iac Arijmhtik'hc Mej'odou}{209}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.3.3}'Elegqoc tou Meg'ejouc B'hmatoc}{210}} \@writefile{toc}{\contentsline {section}{\numberline {9.4}AMESES MEJODOI}{211}} \@writefile{toc}{\contentsline {section}{\numberline {9.5}STIFF DIAFORIKES EXISWSEIS}{214}} \@writefile{toc}{\contentsline {section}{\numberline {9.6}EXETASH ARIJMHTIKWN MEJODWN GIA TIS $ODES$}{216}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.6.1}H M'ejodoc Seir'wn Taylor}{216}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.6.2}Oi M'ejodoi $Runge-Kutta$}{217}} \newlabel{kef9}{{9.6.2}{218}} \@writefile{toc}{\contentsline {chapter}{\numberline {10}Probl'hmata Sunoriak'wn Tim'wn Sun'hjwn Diaforik'wn Exis'wsewn}{219}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {10.1}PROBLHMATA SUNORIAKWN TIMWN}{219}} \newlabel{kef10}{{10.1}{219}} \@writefile{toc}{\contentsline {chapter}{\numberline {11}Merik'ec Diaforik'ec Exis'wseic}{221}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {11.1}MERIKES DIAFORIKES EXISWSEIS}{221}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.1.1}Kathgor'iec Merik'wn Diaforik'wn Exis'wsewn}{221}} \@writefile{toc}{\contentsline {section}{\numberline {11.2}PROBLHMATA ANEXARTHTA APO TON QRONO}{222}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.2.1}Hmidiakrit'ec M'ejodoi Kat'a Th Qr'hsh Peperasm'enwn Diafor'wn}{224}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.2.2}Hmidiakrit'ec M'ejodoi Kat'a Th Qr'hsh Peperasm'enwn Stoiqe'iwn}{225}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.2.3}M'ejodoi Pl'hrouc Diakritopo'ihshc}{226}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.2.4}'Amesec M'ejodoi Peperasm'enwn Diafor'wn}{229}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.2.5}Uperbolik'a 'Enanti Parabolik'wn Problhm'atwn}{230}} \@writefile{toc}{\contentsline {section}{\numberline {11.3}PROBLHMATA POU EXARTWNTAI APO TO QRONO}{233}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.3.1}M'ejodoi Peperasm'enwn Diafor'wn}{233}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.3.2}M'ejodoi Peperasm'enwn Stoiqe'iwn}{235}} \@writefile{toc}{\contentsline {section}{\numberline {11.4}'AMESES MEJODOI GIA ARAIA GRAMMIKA SUSTHMATA}{236}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.4.1}M'ejodoi Arai'hc Paragontopo'ihshc}{236}} \newlabel{kef11}{{11.4.1}{239}} \@writefile{toc}{\contentsline {chapter}{\numberline {12}Taq'uc Metasqhmatism'oc $Fourier$}{241}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {12.1}Parembol'h me Trigwnometrik'ec Sunart'hseic}{241}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.1.1}Suneqe'ic Metasqhmatismo'i $Fourier$}{241}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.1.2}Seir'ec $Fourier$}{241}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.1.3}Diakrito'i Metasqhmatismo'i $Fourier$}{241}} \@writefile{toc}{\contentsline {section}{\numberline {12.2}O ALGORIJMOS $FFT$}{242}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.2.1}Periorismo'i sth Qr'hsh tou $FFT$.}{245}} \@writefile{toc}{\contentsline {section}{\numberline {12.3}EFARMOGES $DFT$}{246}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.3.1}Gr'hgoroc Poluwnumik'oc Pollaplasiasm'oc}{247}} \@writefile{toc}{\contentsline {section}{\numberline {12.4}KUMATAKIA}{249}} \@writefile{toc}{\contentsline {section}{\numberline {12.5}LOGISMIKO GIA $FFT$}{250}} \@writefile{toc}{\contentsline {section}{\numberline {12.6}ISTORIKES SHMEIWSEIS KAI PERAITERW DIABASMA}{250}} \newlabel{kef12}{{12.6}{257}} \@writefile{toc}{\contentsline {chapter}{\numberline {13}Tuqa'ioi Arijmo'i kai Stoqastik'ec Prosomoi'wseic}{259}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {13.1}STOQASTIKES PROSOMOIWSEIS}{259}} \@writefile{toc}{\contentsline {section}{\numberline {13.2}$RANDOMNESS$ KAI TUQAIOI ARIJMOI}{260}} \@writefile{toc}{\contentsline {section}{\numberline {13.3}GENNHTRIES TUQAIWN ARIJMWN}{261}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.3.1}Sugkl'inousec Genn'htriec}{262}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.3.2}Genn'htriec $Fibonacci$}{263}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.3.3}Anomoi'omorfec Katanom'ec}{263}} \citation{*} \bibstyle{plain} \bibdata{Bibliography} \newlabel{kef13}{{13.3.3}{264}} \select@language{english} \@writefile{toc}{\select@language{english}} \@writefile{lof}{\select@language{english}} \@writefile{lot}{\select@language{english}} \bibcite{abramowitz}{1} \bibcite{acton}{2} \bibcite{acton2}{3} \bibcite{ahlberg}{4} \bibcite{alefeld}{5} \bibcite{allgower}{6} \bibcite{ames}{7} \bibcite{lapack}{8} \bibcite{anderson}{9} \bibcite{andrews}{10} \bibcite{ascher}{11} \bibcite{atkinson}{12} \bibcite{axelsson}{13} \bibcite{bank}{14} \bibcite{bard}{15} \bibcite{templates}{16} \bibcite{bartels}{17} \bibcite{barton}{18} \bibcite{texas1}{19} \bibcite{biran}{20} \bibcite{adifor}{21} \bibcite{bjorck}{22} \bibcite{borse}{23} \bibcite{botha}{24} \bibcite{bratley}{25} \bibcite{brenan}{26} \bibcite{brent}{27} \bibcite{briggs_mg}{28} \bibcite{briggs_dft}{29} \bibcite{brigham1}{30} \bibcite{brigham2}{31} \bibcite{brinch_hansen}{32} \bibcite{brinch_hansen2}{33} \bibcite{buchanan}{34} \bibcite{bulirsch}{35} \bibcite{burden_faires}{36} \bibcite{butcher}{37} \bibcite{byrne}{38} \bibcite{texas2}{39} \bibcite{texas3}{40} \bibcite{celia}{41} \bibcite{chatelin_fraysse}{42} \bibcite{chapra_canale}{43} \bibcite{chatelin}{44} \bibcite{cheney_kincaid}{45} \bibcite{childs}{46} \bibcite{chong}{47} \bibcite{cody}{48} \bibcite{cody_fp}{49} \bibcite{coleman}{50} \bibcite{conte_deboor}{51} \bibcite{cowell}{52} \bibcite{crandall}{53} \bibcite{crandall2}{54} \bibcite{cullum}{55} \bibcite{dahlquist}{56} \bibcite{dantzig}{57} \bibcite{datta}{58} \bibcite{davies}{59} \bibcite{davis}{60} \bibcite{davis_rab}{61} \bibcite{deboor}{62} \bibcite{dejong}{63} \bibcite{delves}{64} \bibcite{demmel}{65} \bibcite{nl2sol}{66} \bibcite{dennis_more}{67} \bibcite{dennis_schnabel}{68} \bibcite{deuflhard}{69} \bibcite{deuflhard_hohmann}{70} \bibcite{devries}{71} \bibcite{dierckx}{72} \bibcite{blas3}{73} \bibcite{blas2}{74} \bibcite{linpack}{75} \bibcite{dongarra}{76} \bibcite{ijk}{77} \bibcite{dormand}{78} \bibcite{douglas}{79} \bibcite{dowd}{80} \bibcite{duff}{81} \bibcite{duhamel}{82} \bibcite{engeln}{83} \bibcite{engels}{84} \bibcite{etter2}{85} \bibcite{etter}{86} \bibcite{evans_d}{87} \bibcite{evans_g}{88} \bibcite{faber}{89} \bibcite{fang}{90} \bibcite{farebrother}{91} \bibcite{fatunla}{92} \bibcite{fiacco}{93} \bibcite{fishman}{94} \bibcite{fletcher}{95} \bibcite{fornberg}{96} \bibcite{fmm}{97} \bibcite{forsythe_moler}{98} \bibcite{forsythe_wasow}{99} \bibcite{fosdick}{100} \bibcite{fox}{101} \bibcite{freund}{102} \bibcite{fritsch}{103} \bibcite{gander}{104} \bibcite{eispack2}{105} \bibcite{garcia}{106} \bibcite{garcia_penland}{107} \bibcite{gautschi}{108} \bibcite{gay}{109} \bibcite{gear}{110} \bibcite{gear2}{111} \bibcite{george_liu}{112} \bibcite{gerald_wheatley}{113} \bibcite{npsol}{114} \bibcite{gill1}{115} \bibcite{gill2}{116} \bibcite{giordano}{117} \bibcite{glassey}{118} \bibcite{goldberg}{119} \bibcite{goldfarb}{120} \bibcite{goldfarb_todd}{121} \bibcite{goldstine}{122} \bibcite{golub}{123} \bibcite{golub_oleary}{124} \bibcite{golub_ortega}{125} \bibcite{golub_vanloan}{126} \bibcite{golub_welsch}{127} \bibcite{gottlieb}{128} \bibcite{gould}{129} \bibcite{goult}{130} \bibcite{gourlay}{131} \bibcite{grandine}{132} \bibcite{graps}{133} \bibcite{gupta}{134} \bibcite{gustafsson}{135} \bibcite{haber}{136} \bibcite{hackbusch}{137} \bibcite{hageman}{138} \bibcite{hager}{139} \bibcite{hairer}{140} \bibcite{hall}{141} \bibcite{hammerlin}{142} \bibcite{hammersley}{143} \bibcite{hamming}{144} \bibcite{hanselman}{145} \bibcite{hansen}{146} \bibcite{Heermann}{147} \bibcite{hennell}{148} \bibcite{henrici1}{149} \bibcite{henrici2}{150} \bibcite{higham}{151} \bibcite{higham1}{152} \bibcite{higham2}{153} \bibcite{hill}{154} \bibcite{hopkins}{155} \bibcite{householder_ne}{156} \bibcite{hubbard}{157} \bibcite{ieee_fp}{158} \bibcite{ieee_754}{159} \bibcite{isaacson_keller}{160} \bibcite{iserles}{161} \bibcite{jacobs}{162} \bibcite{jarratt}{163} \bibcite{jenkins_traub1}{164} \bibcite{jenkins_traub2}{165} \bibcite{jennings}{166} \bibcite{jespersen}{167} \bibcite{johnson}{168} \bibcite{joyce}{169} \bibcite{kmn}{170} \bibcite{kaiser}{171} \bibcite{kalos}{172} \bibcite{kaufmann}{173} \bibcite{keller}{174} \bibcite{kelley}{175} \bibcite{kennedy}{176} \bibcite{kincaid_cheney}{177} \bibcite{knuth2}{178} \bibcite{kockler}{179} \bibcite{koonin}{180} \bibcite{koren}{181} \bibcite{krommer}{182} \bibcite{kythe}{183} \bibcite{lambert1}{184} \bibcite{lambert2}{185} \bibcite{landau2}{186} \bibcite{landau1}{187} \bibcite{lapidus_pinder}{188} \bibcite{lapidus_seinfeld}{189} \bibcite{larkin}{190} \bibcite{numal}{191} \bibcite{lawson}{192} \bibcite{blas1}{193} \bibcite{leveque}{194} \bibcite{lindfield}{195} \bibcite{longley}{196} \bibcite{lozier_olver}{197} \bibcite{luenberger}{198} \bibcite{lyness2}{199} \bibcite{lyness3}{200} \bibcite{lyness1}{201} \bibcite{magid}{202} \bibcite{marsaglia}{203} \bibcite{mathews}{204} \bibcite{miller}{205} \bibcite{miller_wrathall}{206} \bibcite{mitchell}{207} \bibcite{moler}{208} \bibcite{moler_morrison}{209} \bibcite{moler_vanloan}{210} \bibcite{moore}{211} \bibcite{moore2}{212} \bibcite{more}{213} \bibcite{minpack}{214} \bibcite{more_sorensen}{215} \bibcite{more_wright}{216} \bibcite{morrison}{217} \bibcite{morton}{218} \bibcite{minos}{219} \bibcite{nakamura}{220} \bibcite{nash}{221} \bibcite{nash_sofer}{222} \bibcite{niederreiter}{223} \bibcite{nievergelt}{224} \bibcite{nocedal}{225} \bibcite{omondi}{226} \bibcite{ortega3}{227} \bibcite{ortega2}{228} \bibcite{ortega1}{229} \bibcite{ostrowski}{230} \bibcite{paige}{231} \bibcite{parlett}{232} \bibcite{part}{233} \bibcite{pereyra}{234} \bibcite{petzold}{235} \bibcite{pickering}{236} \bibcite{quadpack}{237} \bibcite{pratap}{238} \bibcite{nr}{239} \bibcite{ralston}{240} \bibcite{redfern}{241} \bibcite{reinsch1}{242} \bibcite{reinsch2}{243} \bibcite{rice1}{244} \bibcite{rice2}{245} \bibcite{rice3}{246} \bibcite{ellpack}{247} \bibcite{richtmyer}{248} \bibcite{roach}{249} \bibcite{roberts}{250} \bibcite{rubinstein}{251} \bibcite{saad1}{252} \bibcite{saad2}{253} \bibcite{schiesser}{254} \bibcite{schnabel}{255} \bibcite{schumaker}{256} \bibcite{schwarz}{257} \bibcite{srs}{258} \bibcite{shampine}{259} \bibcite{shampine_ode}{260} \bibcite{shampine_allen}{261} \bibcite{shampine_allen_pruess}{262} \bibcite{shampine_gear}{263} \bibcite{shampine_gordon}{264} \bibcite{shampine_watts}{265} \bibcite{shikin}{266} \bibcite{sigmon}{267} \bibcite{skeel1}{268} \bibcite{skeel2}{269} \bibcite{sloan}{270} \bibcite{eispack1}{271} \bibcite{smith}{272} \bibcite{rsmith}{273} \bibcite{sobol}{274} \bibcite{spath}{275} \bibcite{sterbenz}{276} \bibcite{stetter}{277} \bibcite{stewart}{278} \bibcite{stewart2}{279} \bibcite{stewart_sun}{280} \bibcite{stoer_bulirsch}{281} \bibcite{strang_iam}{282} \bibcite{strang_laa}{283} \bibcite{strang_wav}{284} \bibcite{strang_ila}{285} \bibcite{strang_fix}{286} \bibcite{strassen}{287} \bibcite{strikwerda}{288} \bibcite{stroud}{289} \bibcite{stroud_secrest}{290} \bibcite{swann}{291} \bibcite{swarztrauber}{292} \bibcite{taswell}{293} \bibcite{thisted}{294} \bibcite{thomas1}{295} \bibcite{thompson}{296} \bibcite{traub}{297} \bibcite{trefethen}{298} \bibcite{trefethen_bau}{299} \bibcite{vanhuffel}{300} \bibcite{vanloan_fft}{301} \bibcite{vanloan_csm}{302} \bibcite{vanloan_isc}{303} \bibcite{varga}{304} \bibcite{vavasis}{305} \bibcite{vesely}{306} \bibcite{wachpress}{307} \bibcite{wait}{308} \bibcite{walker1}{309} \bibcite{walker2}{310} \bibcite{watkins1}{311} \bibcite{watkins2}{312} \bibcite{watkins3}{313} \bibcite{watson}{314} \bibcite{weaver1}{315} \bibcite{weaver2}{316} \bibcite{wesseling}{317} \bibcite{westlake}{318} \bibcite{wilde}{319} \bibcite{wilkinson}{320} \bibcite{wilkinson1}{321} \bibcite{wilkinson2}{322} \bibcite{handbook}{323} \bibcite{wing}{324} \bibcite{wong}{325} \bibcite{wright}{326} \bibcite{wright_glassman}{327} \bibcite{young}{328} \bibcite{young_gregory}{329} \bibcite{zachary}{330} \bibcite{zhang}{331} \bibcite{zienkiewicz}{332} \bibcite{zlatev}{333} \bibcite{zwillinger}{334}