Home > K25104 > LinearSystems > iteration_analysis.m

iteration_analysis

PURPOSE ^

Calculates the iteration matrix and its eigenvalues

SYNOPSIS ^

function [ H,E ] = iteration_analysis( C,B,w )

DESCRIPTION ^

 Calculates the iteration matrix and its eigenvalues 
   arising from solving the system Ax = b iteratively 
   by splitting A=B+C and Cx=-Bx+b.
 Input arguments:
   C, square matrix
   B, square matrix
   w, relaxation parameter (w=1 gives unrelaxed iterations)
 Output arguments:
   H, iteration matrix 
   E, eigenvalues of the iteration matrix

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [ H,E ] = iteration_analysis( C,B,w )
0002 % Calculates the iteration matrix and its eigenvalues
0003 %   arising from solving the system Ax = b iteratively
0004 %   by splitting A=B+C and Cx=-Bx+b.
0005 % Input arguments:
0006 %   C, square matrix
0007 %   B, square matrix
0008 %   w, relaxation parameter (w=1 gives unrelaxed iterations)
0009 % Output arguments:
0010 %   H, iteration matrix
0011 %   E, eigenvalues of the iteration matrix
0012 
0013 [m,n]=size(C); % find the size of C
0014 if n~= m
0015     error('first input is not a square matrix');
0016 end;
0017 [k,l]=size(B); % find the size of B
0018 if k~= l
0019     error('second input is not a square matrix');
0020 end;
0021 if m~=k
0022     error('matrix dimensions do not agree');
0023 end;
0024     
0025 H=(1-w)*eye(n)-w*inv(C)*B;
0026 E=eig(H);
0027 
0028 end
0029 
0030

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