Templates for the Solution of Linear Systems
19 Aug 2002
04 Dec 2002)
function A = lehmer(n)
%LEHMER 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.
% 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.
A = ones(n,1)*(1:n);
A = A./A';
A = tril(A) + tril(A,-1)';