49 lines
1.5 KiB
Matlab
Executable File
49 lines
1.5 KiB
Matlab
Executable File
%%********************************************************************
|
|
%% igmres: compute ideal GMRES polynomial of deg m
|
|
%% of a matrix B.
|
|
%%
|
|
%% min || p(B) ||_2
|
|
%% where p is a polynomial of degree <= m and p(0) = 1.
|
|
%%
|
|
%% B = a general square matrix.
|
|
%%-----------------------------------------------------------
|
|
%%
|
|
%% [blk,Avec,C,b,X0,y0,Z0,objval,p] = igmres(B,m,feas,solve);
|
|
%%
|
|
%% B = a square matrix.
|
|
%% m = degree of polynomial.
|
|
%% feas = 1 if want feasible starting point
|
|
%% = 0 if otherwise.
|
|
%% solve = 0 just to initialize
|
|
%% = 1 if want to solve the problem.
|
|
%%
|
|
%% p = ideal GMRES polynomial in Matlab format.
|
|
%%*****************************************************************
|
|
%% SDPT3: version 4.0
|
|
%% Copyright (c) 1997 by
|
|
%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
|
|
%% Last Modified: 16 Sep 2004
|
|
%%*****************************************************************
|
|
|
|
function [blk,Avec,C,b,X0,y0,Z0,objval,p] = igmres(B,m,feas,solve)
|
|
|
|
if (nargin <= 3); solve = 0; end;
|
|
if (nargin <= 2); feas = 0; end;
|
|
|
|
N = length(B);
|
|
if (m >= N); error('degree >= size of B'); end;
|
|
|
|
A = cell(1,m+1);
|
|
[V,H,R] = orthbasis(B,m-1);
|
|
A{1} = eye(N);
|
|
for k = [1:m]; A{k+1} = B*V{k}; end;
|
|
[blk,Avec,C,b,X0,y0,Z0,objval,xx] = norm_min(A,feas,solve);
|
|
if (solve)
|
|
y = xx;
|
|
x1 = R(1:m,1:m)*y(1:m);
|
|
p = [x1(m:-1:1); 1];
|
|
else
|
|
objval = []; p = [];
|
|
end
|
|
%%********************************************************************
|