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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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1 function H = hilb(n)
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2 %HILB Hilbert matrix.
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3 % HILB(N) is the N-by-N matrix with elements 1/(i+j-1).
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4 % It is a famous example of a badly conditioned matrix.
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5 % COND(HILB(N)) grows like EXP(3.5*N).
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6 % See INVHILB (standard MATLAB routine) for the exact inverse, which
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7 % has integer entries.
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8 % HILB(N) is symmetric positive definite, totally positive, and a
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9 % Hankel matrix.
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10
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11 % References:
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12 % M.-D. Choi, Tricks or treats with the Hilbert matrix, Amer. Math.
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13 % Monthly, 90 (1983), pp. 301-312.
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14 % N.J. Higham, Accuracy and Stability of Numerical Algorithms,
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15 % Society for Industrial and Applied Mathematics, Philadelphia, PA,
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16 % USA, 1996; sec. 26.1.
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17 % M. Newman and J. Todd, The evaluation of matrix inversion
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18 % programs, J. Soc. Indust. Appl. Math., 6 (1958), pp. 466-476.
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19 % D.E. Knuth, The Art of Computer Programming,
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20 % Volume 1, Fundamental Algorithms, second edition, Addison-Wesley,
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21 % Reading, Massachusetts, 1973, p. 37.
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22
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23 if n == 1
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24 H = 1;
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25 else
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26 H = cauchy( (1:n) - .5);
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27 end