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author Antonio Pino Robles <data.script93@gmail.com>
date Fri, 29 May 2015 09:48:36 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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1 function A = chow(n, alpha, delta)
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Antonio Pino Robles <data.script93@gmail.com>
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2 %CHOW Chow matrix - a singular Toeplitz lower Hessenberg matrix.
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Antonio Pino Robles <data.script93@gmail.com>
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3 % A = CHOW(N, ALPHA, DELTA) is a Toeplitz lower Hessenberg matrix
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Antonio Pino Robles <data.script93@gmail.com>
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4 % A = H(ALPHA) + DELTA*EYE, where H(i,j) = ALPHA^(i-j+1).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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5 % H(ALPHA) has p = FLOOR(N/2) zero eigenvalues, the rest being
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Antonio Pino Robles <data.script93@gmail.com>
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6 % 4*ALPHA*COS( k*PI/(N+2) )^2, k=1:N-p.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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7 % Defaults: ALPHA = 1, DELTA = 0.
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Antonio Pino Robles <data.script93@gmail.com>
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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9 % References:
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Antonio Pino Robles <data.script93@gmail.com>
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10 % T.S. Chow, A class of Hessenberg matrices with known
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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11 % eigenvalues and inverses, SIAM Review, 11 (1969), pp. 391-395.
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Antonio Pino Robles <data.script93@gmail.com>
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12 % G. Fairweather, On the eigenvalues and eigenvectors of a class of
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Antonio Pino Robles <data.script93@gmail.com>
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13 % Hessenberg matrices, SIAM Review, 13 (1971), pp. 220-221.
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Antonio Pino Robles <data.script93@gmail.com>
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14 % I. Singh, G. Poole and T. Boullion, A class of Hessenberg matrices
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Antonio Pino Robles <data.script93@gmail.com>
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15 % with known pseudoinverse and Drazin inverse, Math. Comp.,
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Antonio Pino Robles <data.script93@gmail.com>
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16 % 29 (1975), pp. 615-619.
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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18 if nargin < 3, delta = 0; end
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19 if nargin < 2, alpha = 1; end
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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21 A = toeplitz( alpha.^(1:n), [alpha 1 zeros(1,n-2)] ) + delta*eye(n);