Mercurial > matrix-functions
comparison toolbox/krylov.m @ 2:c124219d7bfa draft
Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
| author | Antonio Pino Robles <data.script93@gmail.com> |
|---|---|
| date | Thu, 07 May 2015 18:36:24 +0200 |
| parents | 8f23314345f4 |
| children |
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| 1:e471a92d17be | 2:c124219d7bfa |
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| 1 function B = krylov(A, x, j) | |
| 2 %KRYLOV Krylov matrix. | |
| 3 % KRYLOV(A, x, j) is the Krylov matrix | |
| 4 % [x, Ax, A^2x, ..., A^(j-1)x], | |
| 5 % where A is an n-by-n matrix and x is an n-vector. | |
| 6 % Defaults: x = ONES(n,1), j = n. | |
| 7 % KRYLOV(n) is the same as KRYLOV(RANDN(n)). | |
| 8 | |
| 9 % Reference: | |
| 10 % G.H. Golub and C.F. Van Loan, Matrix Computations, second edition, | |
| 11 % Johns Hopkins University Press, Baltimore, Maryland, 1989, p. 369. | |
| 12 | |
| 13 [n, n] = size(A); | |
| 14 | |
| 15 if n == 1 % Handle special case A = scalar. | |
| 16 n = A; | |
| 17 A = randn(n); | |
| 18 end | |
| 19 | |
| 20 if nargin < 3, j = n; end | |
| 21 if nargin < 2, x = ones(n,1); end | |
| 22 | |
| 23 | |
| 24 B = ones(n,j); | |
| 25 B(:,1) = x(:); | |
| 26 for i=2:j | |
| 27 B(:,i) = A*B(:,i-1); | |
| 28 end |