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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 = lehmer(n)
2 %LEHMER Lehmer matrix - symmetric positive definite.
3 % A = LEHMER(N) is the symmetric positive definite N-by-N matrix with
4 % A(i,j) = i/j for j >= i.
5 % A is totally nonnegative. INV(A) is tridiagonal, and explicit
6 % formulas are known for its entries.
7 % N <= COND(A) <= 4*N*N.
8
9 % References:
10 % M. Newman and J. Todd, The evaluation of matrix inversion
11 % programs, J. Soc. Indust. Appl. Math., 6 (1958), pp. 466-476.
12 % Solutions to problem E710 (proposed by D.H. Lehmer): The inverse
13 % of a matrix, Amer. Math. Monthly, 53 (1946), pp. 534-535.
14 % J. Todd, Basic Numerical Mathematics, Vol. 2: Numerical Algebra,
15 % Birkhauser, Basel, and Academic Press, New York, 1977, p. 154.
16
17 A = ones(n,1)*(1:n);
18 A = A./A';
19 A = tril(A) + tril(A,-1)';