www.gusucode.com > elmat工具箱matlab源码程序 > elmat/private/chow.m
function A = chow(n, alpha, delta, classname) %CHOW Chow matrix (singular Toeplitz lower Hessenberg matrix). % A = GALLERY('CHOW',N,ALPHA,DELTA) returns A such that % A = H(ALPHA) + DELTA*EYE, where H(i,j) = ALPHA^(i-j+1). % H(ALPHA) has p = FLOOR(N/2) zero eigenvalues, the rest being % 4*ALPHA*COS( k*PI/(N+2) )^2, k=1:N-p. % Defaults: ALPHA = 1, DELTA = 0. % References: % [1] T. S. Chow, A class of Hessenberg matrices with known eigenvalues % and inverses, SIAM Review, 11 (1969), pp. 391-395. % [2] G. Fairweather, On the eigenvalues and eigenvectors of a class of % Hessenberg matrices, SIAM Review, 13 (1971), pp. 220-221. % [3] I. Singh, G. Poole and T. Boullion, A class of Hessenberg matrices % with known pseudoinverse and Drazin inverse, Math. Comp., 29 (1975), % pp. 615-619. % % Nicholas J. Higham % Copyright 1984-2005 The MathWorks, Inc. if isempty(alpha), alpha = ones(classname); end if isempty(delta), delta = zeros(classname); end A = toeplitz( alpha.^(1:n), [alpha 1 zeros(1,n-2,classname)] ) + ... delta*eye(n,classname);