chiziqli algebraik tenglamalar sistemasini yechishning iteratsion usullari

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gauss-seidel method chiziqli algebraik tenglamalar sistemasini yechimini topishning iteratsion usullari 1 n ta nomalumli n ta tenglamalar sistemasi berilgan: 11313212111 ... bxaxaxaxa nn =++++ 2323222121 ... bxaxaxaxa n2n =++++ nnnnnnn bxaxaxaxa =++++ ...332211 . . . . . . 2 3 ta nomalumli 3 ta tenglamalar sistemasi berilgan: 11 1 12 2 13 3 1a x a x a x b+ + = 21 1 22 2 23 3 2a x a x a x b+ + = 31 1 32 2 33 3 3a x a x a x b+ + = 3 diagonal elementlari noldan farqli bo’lishi kerak. 4 iteratsion formulaning yaqinlashuvchi bo’lish sharti 11 12 13a a a≥ + 22 21 23a a a≥ + 33 31 32a a a≥ + n ta nomalumli n ta tenglamalar sistemasi uchun: 5 iteratsion formulaning yaqinlashuvchi bo’lish sharti 1 n ii ij j j i a a = ≠ ≥∑ …

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3 7.85 0.1 0.2 3 19.3 0.1 0 0,19071 6,51850 3,05759 6,73333 6,5185.3 7 71.4 0.3 0.2 1 0 2,57397 6,73333 0,19071 6,94181 0 x x x + + = = − − + = = − + = = − 15 1 1 1 2 1 3 2.616667 2.794524 7.005610 x x x = = − = 2 1 2 2 2 3 2.990557 2.499625 7.000291 x x x = = − = birinchi iteratsiya ikkinchi iteratsiya [ ]  75.23 −=txaniq yechim: gaus-zeidel iteratsion formulasi nnnnnn nn nn bxaxaxa bxaxaxa bxaxaxa =+++ =+++ =+++     2211 22222121 11212111               = 0 0 2 0 1 0 nx x x x  gaus-zeidel iteratsion formulasi nnnnnn nn nn bxaxaxa bxaxaxa bxaxaxa =+++ =+++ =+++     2211 22222121 11212111   …

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iteratsion formulaning yaqinlashuvchi bo’lish sharti yakobi usuli slide number 7 yakobi usuli slide number 9 slide number 10 slide number 11 slide number 12 slide number 13 slide number 14 slide number 15 gaus-zeidel iteratsion formulasi gaus-zeidel iteratsion formulasi gaus-zeidel iteratsion formulasi slide number 19 slide number 20 slide number 21 slide number 22 slide number 23 slide number 24

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gauss-seidel method chiziqli algebraik tenglamalar sistemasini yechimini topishning iteratsion usullari 1 n ta nomalumli n ta tenglamalar sistemasi berilgan: 11313212111 ... bxaxaxaxa nn =++++ 2323222121 ... bxaxaxaxa n2n =++++ nnnnnnn bxaxaxaxa =++++ ...332211 . . . . . . 2 3 ta nomalumli 3 ta tenglamalar sistemasi berilgan: 11 1 12 2 13 3 1a x a x a x b+ + = 21 1 22 2 23 3 2a x a x a x b+ + = 31 1 32 2 33 3 3a x a x a x b+ + = 3 diagonal elementlari noldan farqli bo’lishi kerak. 4 iteratsion formulaning yaqinlashuvchi bo’lish sharti 11 12 13a a a≥ + 22 21 23a a a≥ + 33 31 …

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