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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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1 function A = parter(n)
2 %PARTER Parter matrix - a Toeplitz matrix with singular values near PI.
3 % PARTER(N) is the matrix with (i,j) element 1/(i-j+0.5).
4 % It is a Cauchy matrix and a Toeplitz matrix.
5
6 % At the Second SIAM Conference on Linear Algebra, Raleigh, N.C.,
7 % 1985, Cleve Moler noted that most of the singular values of
8 % PARTER(N) are very close to PI. An explanation of the phenomenon
9 % was given by Parter; see also the paper by Tyrtyshnikov.
10 %
11 % References:
12 % The MathWorks Newsletter, Volume 1, Issue 1, March 1986, page 2.
13 % S.V. Parter, On the distribution of the singular values of Toeplitz
14 % matrices, Linear Algebra and Appl., 80 (1986), pp. 115-130.
15 % E.E. Tyrtyshnikov, Cauchy-Toeplitz matrices and some applications,
16 % Linear Algebra and Appl., 149 (1991), pp. 1-18.
17
18 A = cauchy( (1:n)+0.5, -(1:n) );