dir    templates
for     Base Directory

file    bicg.m
for     function [x, error, iter, flag] = bicg(A, x, b, M, max_it, tol)
,       
,       %  -- Iterative template routine --
,       %     Univ. of Tennessee and Oak Ridge National Laboratory
,       %     October 1, 1993
,       %     Details of this algorithm are described in "Templates for the
,       %     Solution of Linear Systems: Building Blocks for Iterative
,       %     Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
,       %     Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
,       %     1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
size    2445

file    bicgstab.m
for     function [x, error, iter, flag] = bicgstab(A, x, b, M, max_it, tol)
,       
,       %  -- Iterative template routine --
,       %     Univ. of Tennessee and Oak Ridge National Laboratory
,       %     October 1, 1993
,       %     Details of this algorithm are described in "Templates for the
,       %     Solution of Linear Systems: Building Blocks for Iterative
,       %     Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
,       %     Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
,       %     1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
size    2922

file    cg.m
for     function [x, error, iter, flag] = cg(A, x, b, M, max_it, tol)
,       
,       %  -- Iterative template routine --
,       %     Univ. of Tennessee and Oak Ridge National Laboratory
,       %     October 1, 1993
,       %     Details of this algorithm are described in "Templates for the
,       %     Solution of Linear Systems: Building Blocks for Iterative
,       %     Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
,       %     Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
,       %     1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
size    2091

file    cgs.m
for     function [x, error, iter, flag] = cgs(A, x, b, M, max_it, tol)
,       
,       %  -- Iterative template routine --
,       %     Univ. of Tennessee and Oak Ridge National Laboratory
,       %     October 1, 1993
,       %     Details of this algorithm are described in "Templates for the
,       %     Solution of Linear Systems: Building Blocks for Iterative
,       %     Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
,       %     Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
,       %     1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
size    2367

file    cheby.m
for     function [x, error, iter, flag] = cheby(A, x, b, M, max_it, tol)
,       
,       %  -- Iterative template routine --
,       %     Univ. of Tennessee and Oak Ridge National Laboratory
,       %     October 1, 1993
,       %     Details of this algorithm are described in "Templates for the
,       %     Solution of Linear Systems: Building Blocks for Iterative
,       %     Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
,       %     Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
,       %     1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
size    2169

file    gmres.m
for     function [x, error, iter, flag] = gmres( A, x, b, M, restrt, max_it, tol )
,       
,       %  -- Iterative template routine --
,       %     Univ. of Tennessee and Oak Ridge National Laboratory
,       %     October 1, 1993
,       %     Details of this algorithm are described in "Templates for the
,       %     Solution of Linear Systems: Building Blocks for Iterative
,       %     Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
,       %     Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
,       %     1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
size    3389

file    jacobi.m
for     function [x, error, iter, flag]  = jacobi(A, x, b, max_it, tol)
,       
,       %  -- Iterative template routine --
,       %     Univ. of Tennessee and Oak Ridge National Laboratory
,       %     October 1, 1993
,       %     Details of this algorithm are described in "Templates for the
,       %     Solution of Linear Systems: Building Blocks for Iterative
,       %     Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
,       %     Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
,       %     1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
size    1809

file    lehmer.m
for     function A = lehmer(n)
,       %LEHMER  A = LEHMER(N) is the symmetric positive definite N-by-N matrix with
,       %                         A(i,j) = i/j for j>=i.
,       %        A is totally nonnegative.  INV(A) is tridiagonal, and explicit
,       %        formulas are known for its entries.
,       %        N <= COND(A) <= 4*N*N.
,       
,       %        References:
,       %        M. Newman and J. Todd, The evaluation of matrix inversion
,       %        programs, J. Soc. Indust. Appl. Math., 6 (1958), pp. 466-476.
size    659

file    makefish.m
for     function mat = makefish(siz);
,       % make a Poisson matrix
,       
,       leng = siz*siz;
,       dia = zeros(siz,siz);
,       off = -eye(siz,siz);
,        for i=1:siz, dia(i,i)=4; end;
,        for i=1:siz-1, dia(i,i+1)=-1; dia(i+1,i)=-1; end;
,       mat = zeros(leng,leng);
,        for ib=1:siz,
size    432

file    matgen.m
for     function mat = testmat( siz );
,       %
,       % matrix generator function for templates tester
,       %
,          if ( siz == 10 ),
,             mat = makefish( 4 );           % poisson matrix
,          elseif ( siz == 20  ),
,             mat = wathen( 3, 3, 0 );       % spd consistent mass matrix
,          elseif ( siz == 30  ),
,             mat = wathen( 3, 3, 1 );       % spd consistent mass matrix
size    526

file    qmr.m
for     function [x, error, iter, flag] = qmr( A, x, b, M, max_it, tol )
,       
,       %  -- Iterative template routine --
,       %     Univ. of Tennessee and Oak Ridge National Laboratory
,       %     October 1, 1993
,       %     Details of this algorithm are described in "Templates for the
,       %     Solution of Linear Systems: Building Blocks for Iterative
,       %     Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
,       %     Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
,       %     1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
size    3862

file    rotmat.m
for     function [ c, s ] = rotmat( a, b )
,       
,       %
,       % Compute the Givens rotation matrix parameters for a and b.
,       %
,          if ( b == 0.0 ),
,             c = 1.0;
,             s = 0.0;
,          elseif ( abs(b) > abs(a) ),
,             temp = a / b;
size    353

file    sor.m
for     function [x, error, iter, flag]  = sor(A, x, b, w, max_it, tol)
,       
,       %  -- Iterative template routine --
,       %     Univ. of Tennessee and Oak Ridge National Laboratory
,       %     October 1, 1993
,       %     Details of this algorithm are described in "Templates for the
,       %     Solution of Linear Systems: Building Blocks for Iterative
,       %     Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
,       %     Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
,       %     1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
size    1921

file    split.m
for     function [ M, N, b ] = split( A, b, w, flag )
,       %
,       % function [ M, N, b ] = split( A, b, w, flag )
,       %
,       % split.m sets up the matrix splitting for the stationary
,       % iterative methods: jacobi and sor (gauss-seidel when w = 1.0 )
,       %
,       % input   A        DOUBLE PRECISION matrix
,       %         b        DOUBLE PRECISION right hand side vector (for SOR)
,       %         w        DOUBLE PRECISION relaxation scalar
size    1027

file    tester.m
for     function test_it = templatestester()
,       %
,       % function[ test_it ] = templatestester()
,       %
,       % templatestester loops over the various MatLab versions of the iterative
,       % templates. Test matrices are generated in matgen.m. Results are printed 
,       % to the screen.
,       
,       %  INITIALIZATION
,       
size    9419

file    wathen.m
for     function A = wathen(nx, ny, k)
,       %WATHEN  A = WATHEN(NX,NY) is a random N-by-N finite element matrix
,       %        where N = 3*NX*NY + 2*NX + 2*NY + 1.
,       %        A is precisely the "consistent mass matrix" for a regular NX-by-NY
,       %        grid of 8-node (serendipity) elements in 2 space dimensions.
,       %        A is symmetric positive definite for any (positive) values of 
,       %        the "density", RHO(NX,NY), which is chosen randomly in this routine.
,       %        In particular, if D=DIAG(DIAG(A)), then 
,       %              0.25 <= EIG(INV(D)*A) <= 4.5
,       %        for any positive integers NX and NY and any densities RHO(NX,NY).
size    1687

file    README
for     
,       ============= README file for testing the Iterative Templates ==================
,       Version 1.0 November 1, 1993.
,       
,       This file contains the MATLAB versions of the algorithms discussed in
,       the book ``Templates for the Solution of Linear Systems: Building Blocks 
,       for Iterative Methods'', by Richard Barrett, Michael Berry, Tony F. Chan, 
,       James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, 
,       Charles Romine, and Henk Van der Vorst, SIAM Publication, 1993.
,       In addition, there are test routine that a user can execute 
size    3931