www.gusucode.com > elmat工具箱matlab源码程序 > elmat/private/lehmer.m
function A = lehmer(n,classname) %LEHMER Lehmer matrix. % A = GALLERY('LEHMER',N) is the symmetric positive definite % N-by-N matrix such that A(i,j) = i/j for j >= i. % % Properties: % A is totally nonnegative. % INV(A) is tridiagonal and explicitly known. % A.^r is symmetric positive semidefinite for all nonnegative r. % N <= COND(A) <= 4*N*N. % References: % [1] R. Bhatia, Infinitely divisible matrices, Amer. Math. Monthly, % 133 (2006), pp. 221-235. (For the "A.^r" property.) % [2] M. Newman and J. Todd, The evaluation of matrix inversion % programs, J. Soc. Indust. Appl Math, 6 (1958),pp. 466-476. % [3] Solutions to problem E710 (proposed by D.H. Lehmer): % The inverse of a matrix, Amer. Math. Monthly, 53 (1946), % pp. 534-535. % [4] J. Todd, Basic Numerical Mathematics, Vol. 2: Numerical % Algebra, Birkhauser, Basel, and Academic Press, New York, % 1977, p. 154. % % Nicholas J. Higham % Copyright 1984-2015 The MathWorks, Inc. a = 1:cast(n,classname); A = a ./ a'; A = tril(A) + tril(A,-1)';