Mercurial > matrix-functions
view toolbox/lehmer.m @ 2:c124219d7bfa draft
Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author | Antonio Pino Robles <data.script93@gmail.com> |
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date | Thu, 07 May 2015 18:36:24 +0200 |
parents | 8f23314345f4 |
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function A = lehmer(n) %LEHMER Lehmer matrix - symmetric positive definite. % A = LEHMER(N) is the symmetric positive definite N-by-N matrix with % A(i,j) = i/j for j >= i. % A is totally nonnegative. INV(A) is tridiagonal, and explicit % formulas are known for its entries. % N <= COND(A) <= 4*N*N. % References: % M. Newman and J. Todd, The evaluation of matrix inversion % programs, J. Soc. Indust. Appl. Math., 6 (1958), pp. 466-476. % Solutions to problem E710 (proposed by D.H. Lehmer): The inverse % of a matrix, Amer. Math. Monthly, 53 (1946), pp. 534-535. % J. Todd, Basic Numerical Mathematics, Vol. 2: Numerical Algebra, % Birkhauser, Basel, and Academic Press, New York, 1977, p. 154. A = ones(n,1)*(1:n); A = A./A'; A = tril(A) + tril(A,-1)';