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comparison toolbox/clement.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
equal deleted inserted replaced
1:e471a92d17be 2:c124219d7bfa
1 function A = clement(n, k)
2 %CLEMENT Clement matrix - tridiagonal with zero diagonal entries.
3 % CLEMENT(N, K) is a tridiagonal matrix with zero diagonal entries
4 % and known eigenvalues. It is singular if N is odd. About 64
5 % percent of the entries of the inverse are zero. The eigenvalues
6 % are plus and minus the numbers N-1, N-3, N-5, ..., (1 or 0).
7 % For K = 0 (the default) the matrix is unsymmetric, while for
8 % K = 1 it is symmetric.
9 % CLEMENT(N, 1) is diagonally similar to CLEMENT(N).
10
11 % Similar properties hold for TRIDIAG(X,Y,Z) where Y = ZEROS(N,1).
12 % The eigenvalues still come in plus/minus pairs but they are not
13 % known explicitly.
14 %
15 % References:
16 % P.A. Clement, A class of triple-diagonal matrices for test
17 % purposes, SIAM Review, 1 (1959), pp. 50-52.
18 % A. Edelman and E. Kostlan, The road from Kac's matrix to Kac's
19 % random polynomials. In John~G. Lewis, editor, Proceedings of
20 % the Fifth SIAM Conference on Applied Linear Algebra Society
21 % for Industrial and Applied Mathematics, Philadelphia, 1994,
22 % pp. 503-507.
23 % O. Taussky and J. Todd, Another look at a matrix of Mark Kac,
24 % Linear Algebra and Appl., 150 (1991), pp. 341-360.
25
26 if nargin == 1, k = 0; end
27
28 n = n-1;
29
30 x = n:-1:1;
31 z = 1:n;
32
33 if k == 0
34 A = diag(x, -1) + diag(z, 1);
35 else
36 y = sqrt(x.*z);
37 A = diag(y, -1) + diag(y, 1);
38 end