NumeriÄka linearna algebra - Odjel za matematiku - SveuÄiliÅ¡te ...

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iiSADRŽAJ2.3.23 Osnovne grafičke naredbe . . . . . . . . . . . . . . . . 382.3.24 Linijski prikaz podataka . . . . . . . . . . . . . . . . . 382.3.25 Točkasti prikaz podataka . . . . . . . . . . . . . . . . . 403 Složenost algoritama 433.1 Složenost računanja . . . . . . . . . . . . . . . . . . . . . . . . 434 Stabilnost i uvjetovanost 474.1 Pogreške . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.1.1 Stabilnost i točnost . . . . . . . . . . . . . . . . . . . . 494.2 Uvjetovanost . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 Sustavi linearnih jednadžbi 575.1 Gaussove eliminacije . . . . . . . . . . . . . . . . . . . . . . . 575.2 Numerička svojstva Gaussovih eliminacija . . . . . . . . . . . 665.2.1 Analiza pogreške Gaussovih eliminacija . . . . . . . . . 685.3 Gaussove eliminacije s djelomičnim pivotiranjem . . . . . . . . 695.3.1 Analiza pogreške za GEDP . . . . . . . . . . . . . . . . 735.4 QR dekompozicija . . . . . . . . . . . . . . . . . . . . . . . . . 785.4.1 Householderova QR dekompozicija (Householderovi reflektori). . . . . . . . . . . . . . . . . . . . . . . . . . 815.4.2 Broj računskih operacija (trošak računanja) . . . . . . 845.4.3 Analiza točnosti . . . . . . . . . . . . . . . . . . . . . . 876 Iterativne metode 916.1 Linearne metode . . . . . . . . . . . . . . . . . . . . . . . . . 916.1.1 Jacobijeva metoda . . . . . . . . . . . . . . . . . . . . 956.1.2 Gauss-Seidelova metoda . . . . . . . . . . . . . . . . . 976.2 Metoda najbržeg silaska i konjugiranih gradijenata . . . . . . 996.2.1 Metoda najbržeg silaska . . . . . . . . . . . . . . . . . 1026.2.2 Metoda konjugiranih gradijenata . . . . . . . . . . . . 1037 Problem najmanjih kvadrata 1077.1 Normalne jednadžbe . . . . . . . . . . . . . . . . . . . . . . . 1097.2 Rješavanje LPNK pomoću SVD dekompozicije . . . . . . . . . 1117.2.1 Dekompozicija na singularne vrijednosti . . . . . . . . 1117.2.2 Rješavanje LPNK pomoću dekompozicije na singularnevrijednosti . . . . . . . . . . . . . . . . . . . . . . . . . 114
SADRŽAJiii7.2.3 Rješavanje LPNK pomoću QR dekompozicije . . . . . 1167.3 Uvjetovanost problema najmanjih kvadrata . . . . . . . . . . . 1188 Svojstvene vrijednosti i svojstveni vektori 1238.1 Problem svojstvenih vrijednosti . . . . . . . . . . . . . . . . . 1238.1.1 Iterativne metode za simetrične matrice . . . . . . . . 126Literatura 135Indeks 136
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46 3. Složenost algoritama
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48 4. Stabilnost i uvjetovanostpost
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50 4. Stabilnost i uvjetovanostU na
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52 4. Stabilnost i uvjetovanostKroz
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54 4. Stabilnost i uvjetovanostPret
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56 4. Stabilnost i uvjetovanostje p
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58 5. Sustavi linearnih jednadžbid
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60 5. Sustavi linearnih jednadžbiv
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62 5. Sustavi linearnih jednadžbiP
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70 5. Sustavi linearnih jednadžbiP
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76 5. Sustavi linearnih jednadžbiV
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80 5. Sustavi linearnih jednadžbis
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86 5. Sustavi linearnih jednadžbiU
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88 5. Sustavi linearnih jednadžbiT
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90 5. Sustavi linearnih jednadžbi
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92 6. Iterativne metodestoga za taj
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94 6. Iterativne metodeoblika matri
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96 6. Iterativne metodeTeorem 6.3a)
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98 6. Iterativne metodeTeorem 6.4 A
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100 6. Iterativne metodepa je a 0
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102 6. Iterativne metodeilix k = x
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104 6. Iterativne metodešto nakon
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106 6. Iterativne metode
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108 7. Problem najmanjih kvadratasu
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110 7. Problem najmanjih kvadrata0
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112 7. Problem najmanjih kvadrataTe
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114 7. Problem najmanjih kvadratab)
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116 7. Problem najmanjih kvadrataBu
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118 7. Problem najmanjih kvadrataTa
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120 7. Problem najmanjih kvadrataTe
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122 7. Problem najmanjih kvadrata
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124 8. Svojstvene vrijednosti i svo
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