krylov子空间法 krylov子空间方法的程序实现，用于解高阶矩阵-Matlab Codes for Krylov subspace methods

1. MINRES method by Paige and Saunders　implementation

function [ x, istop, itn, rnorm, Arnorm, Anorm, Acond, ynorm ] = ...

minres( A, b, M, shift, show, check, itnlim, rtol )

　[ x, istop, itn, rnorm, Arnorm, Anorm, Acond, ynorm ] = ...

　minres( A, b, M, shift, show, check, itnlim, rtol )



　minres solves the n x n system of linear equations Ax = b

　or the n x n least squares problem min ||Ax- b||_2^2,

　where A is a symmetric matrix (possibly indefinite or singular)

　and b is a given vector. The dimension n is defined by length(b).



　INPUT:



　 A　may be a dense or sparse matrix (preferably sparse!)

　or a function handle such that y = A(x) returns the product

　y = A*x for any given n-vector x.



　If M = [], preconditioning is not used. Otherwise,

　 M　defines a positive-definite preconditioner M = C*C .

　 M　may be a dense or sparse matrix (preferably sparse!)

　or a function handle such that y = M(x) solves th