Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc21762/doc.pdf Дата изменения: Wed Jul 30 16:31:18 2008 Дата индексирования: Mon Oct 1 21:43:34 2012 Кодировка:

. ., . . : , . , . C Ax = b, (1) A m x m, m , m 1, x, b - Rm. 1. , A (W), k(A) A , W = {-s} U [,M], 0 < s, 0 < < M. 1. A m x m (W), , .. det A A . . A m x m det A k(A) k 1 m, . [1]. W , k(A) . . 2. A (W). (1), . . 1 A (W), , 2 [1]. 2. , xn - Rm : xn+1 = Bxn ­ Cb, n = 0,1,..., B = E+A+A2, C = E+A, (2) , , , . (,,) = 1 + + 2, q(,) = supW |(,,)|. 3. A (W). k() B : k() = (,, k(A)), m k 1. . - vk Rm A k(A) R vk ,


.. Avk = k(A)vk. A , A2vk = k(A)vk = k(A)k(A)vk = (k(A))2vk. , - vk A2 k(A2) = k2(A). E - v (E) = 1. , , A2 vk, , B k() (,, k(A)). 4. q(,) < 1 A (W). (2) . . q(,) < 1, k(B), m k 1, B |k(B)| < 1. (2) |k(B)| < 1), m k 1 [2]. 5. (2) x*. (A) -/, - x* Rm (1). . (2). x* = Cb. , C . , C , - u Rm, Cu = 0, .. u + Au = 0 . - u (A) = - /, 0. C. C , -1. -1 x* = Cb, x* = b. x* (1). 6. A (W) q(,) < 1. (A) -/. . , (A) = - /, (B) = 1, q(,) < 1. 4,5,6 7. 7. A (W) q(,) < 1. (2) (1). 3. (2) c 0, 0 , q(0,0) = inf, q(,), q(0 , 0) 0. 8. 0 = - 2/(s+Ms-M+M2) 0 = (s-)0. |(0,0,)| 1 + s0 W, .. = -s, = = M . . (0,0,) = 0 = ( ­ s)/2, W. (0,0,) > 0 , .. (0,0,M) < (0,0,) < (0,0, ) < < M. 0 = (s-)0 (0,0,) , W, (0,0,-s) =(0,0,)=1+s0 > 0, (0,0,M) = 1+(Ms-M+M2)0 = -1 - s0. -


|(0,0,)| W = -s, = = M. 9. A (W). (2) 0 = - 2/(s+Ms-M+M2), 0 = (s-)0 (1) , (0 , 0) = 1 + s0. . 8 q(0,0) = supW |(,,)| = 1 + s0 > 0. . , , .. 1 1 , q(1,1) < q(0,0). (3) - s, M (3) 0 0, - 1 + s0 - s20 < 1 ­ s1 +s21 < 1 ­ s0 +s20, - 1 - 0 - 20 < 1 + 1 + 21 < 1 + 0 + 20, 1 + M0 + M20 < - 1 - M1 - M21 < - 1 - M0 - M20. (4) (5) (6)

(4) (5) (6) , - 2 + s0 - s20 < ­ s1 +s21 < ­ s0 + s20, - 2 - 0 - 0 < 1 + 1 < 0 + 0, 2 + M0 + M 0 < - M1 - M 1 < - M0 - M 0. -2( + s) ­ s( + s)0 < s ( + s)1 < s( + s)0 - ( 0 + 2/ (s)) < 1 < 0
. . 2 2 2 2 2 2

(7) (8) (9) (10) (11)

(7) , (8) s , s( + s) > 0, (10) (8) M, (9) , -2(M - ) + M(M - )0 < - M(M - )1 < - M(M - )0 - 0 + 2/(M) > 1 > 0
. .

(12) (13)

0 < < M, - M(M - ) < 0 (12) (11) , 1 < 0, (13) , 1 > 0. . 9 0 = 1/7, 0 = - 1/7, s = 1, = 2 M = 4 [3].
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1. .. . .: , . . -. ., 1971. 432 . 2. .., .., .. . . .: , . . -. ., 1987. 600 . 3. .., .. // . 14 ­ ". . ", . ... - : " ", 2007, . 2. . 111 ­ 117.

OPTIMUM METHOD OF SIMPLE ITERATION GENERATED BY OPERATOR WITH ALL POSITIVE EIGEN VALUES EXCEPT ONE NEGATIVE VALUE Sorokin P. N., Chentsova N. N. Optimum method of simple iteration for generating operator with eigen values of different sings: one negative and other positive is obtained. Negative value is given, positive values belong to segment. Optimum method in norm C is searched out in the class of two-parametric family of methods of simple iteration