function A = lehmer(n)%% A matrix generator for iterative templates tester.%% 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.%%        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.%% ============================================================================  A = ones(n,1)*(1:n);  A = A./A';  A = tril(A) + tril(A,-1)';% ------------% End lehmer.m% ------------