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function A = poisson(n,classname) %POISSON Block tridiagonal matrix from Poisson's equation (sparse). % GALLERY('POISSON',N) is the block tridiagonal (sparse) matrix % of order N^2 resulting from discretizing Poisson's equation with % the 5-point operator on an N-by-N mesh. The matrix is symmettric % positive definite and has eigenvalues % 2*( 2 - cos(pi*i/(N+1)) - cos(pi*j/(N+1)) ), i = 1:N, j = 1:N. % Reference: % G. H. Golub and C. F. Van Loan, Matrix Computations, third edition, % Johns Hopkins University Press, Baltimore, Maryland, 1996, % Sec. 4.5.4. % % Nicholas J. Higham % Copyright 1984-2008 The MathWorks, Inc. S = tridiag(n,-1,2,-1,classname); I = speye(n); A = kron(I,S) + kron(S,I);