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comparison toolbox/chow.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +0200
parents 8f23314345f4
children
comparison
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1:e471a92d17be 2:c124219d7bfa
1 function A = chow(n, alpha, delta)
2 %CHOW Chow matrix - a singular Toeplitz lower Hessenberg matrix.
3 % A = CHOW(N, ALPHA, DELTA) is a Toeplitz lower Hessenberg matrix
4 % A = H(ALPHA) + DELTA*EYE, where H(i,j) = ALPHA^(i-j+1).
5 % H(ALPHA) has p = FLOOR(N/2) zero eigenvalues, the rest being
6 % 4*ALPHA*COS( k*PI/(N+2) )^2, k=1:N-p.
7 % Defaults: ALPHA = 1, DELTA = 0.
8
9 % References:
10 % T.S. Chow, A class of Hessenberg matrices with known
11 % eigenvalues and inverses, SIAM Review, 11 (1969), pp. 391-395.
12 % G. Fairweather, On the eigenvalues and eigenvectors of a class of
13 % Hessenberg matrices, SIAM Review, 13 (1971), pp. 220-221.
14 % I. Singh, G. Poole and T. Boullion, A class of Hessenberg matrices
15 % with known pseudoinverse and Drazin inverse, Math. Comp.,
16 % 29 (1975), pp. 615-619.
17
18 if nargin < 3, delta = 0; end
19 if nargin < 2, alpha = 1; end
20
21 A = toeplitz( alpha.^(1:n), [alpha 1 zeros(1,n-2)] ) + delta*eye(n);