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function G = grcar(n, k, classname) %GRCAR Grcar matrix. % GALLERY('GRCAR',N,K) is an N-by-N Toeplitz matrix with -1s on % the subdiagonal, 1s on the diagonal, and K superdiagonals of 1s. % The default is K = 3. The eigenvalues are sensitive. % References: % [1] J. F. Grcar, Operator coefficient methods for linear equations, % Report SAND89-8691, Sandia National Laboratories, Albuquerque, % New Mexico, 1989 (Appendix 2). % [2] N. M. Nachtigal, L. Reichel and L. N. Trefethen, A hybrid GMRES % algorithm for nonsymmetric linear systems, SIAM J. Matrix Anal. % Appl., 13 (1992), pp. 796-825. % % Copyright 1984-2005 The MathWorks, Inc. if isempty(k), k = 3; end G = tril(triu(ones(n,classname)), k) - diag(ones(n-1,1,classname), -1);