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comparison toolbox/lesp.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 T = lesp(n)
2 %LESP A tridiagonal matrix with real, sensitive eigenvalues.
3 % LESP(N) is an N-by-N matrix whose eigenvalues are real and smoothly
4 % distributed in the interval approximately [-2*N-3.5, -4.5].
5 % The sensitivities of the eigenvalues increase exponentially as
6 % the eigenvalues grow more negative.
7 % The matrix is similar to the symmetric tridiagonal matrix with
8 % the same diagonal entries and with off-diagonal entries 1,
9 % via a similarity transformation with D = diag(1!,2!,...,N!).
10
11 % References:
12 % H.W.J. Lenferink and M.N. Spijker, On the use of stability regions in
13 % the numerical analysis of initial value problems,
14 % Math. Comp., 57 (1991), pp. 221-237.
15 % L.N. Trefethen, Pseudospectra of matrices, in Numerical Analysis 1991,
16 % Proceedings of the 14th Dundee Conference,
17 % D.F. Griffiths and G.A. Watson, eds, Pitman Research Notes in
18 % Mathematics, volume 260, Longman Scientific and Technical, Essex,
19 % UK, 1992, pp. 234-266.
20
21 x = 2:n;
22 T = full(tridiag( ones(size(x))./x, -(2*[x n+1]+1), x));