Mercurial > matrix-functions
view toolbox/prolate.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> |
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date | Thu, 07 May 2015 18:36:24 +0200 |
parents | 8f23314345f4 |
children |
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function A = prolate(n, w) %PROLATE Prolate matrix - symmetric, ill-conditioned Toeplitz matrix. % A = PROLATE(N, W) is the N-by-N prolate matrix with parameter W. % It is a symmetric Toeplitz matrix. % If 0 < W < 0.5 then % - A is positive definite % - the eigenvalues of A are distinct, lie in (0, 1), and % tend to cluster around 0 and 1. % W defaults to 0.25. % Reference: % J.M. Varah. The Prolate matrix. Linear Algebra and Appl., % 187:269--278, 1993. if nargin == 1, w = 0.25; end a = zeros(n,1); a(1) = 2*w; a(2:n) = sin( 2*pi*w*(1:n-1) ) ./ ( pi*(1:n-1) ); A = toeplitz(a);