Mercurial > matrix-functions
comparison toolbox/hilb.m @ 0:8f23314345f4 draft
Create local repository for matrix toolboxes. Step #0 done.
| author | Antonio Pino Robles <data.script93@gmail.com> |
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| date | Wed, 06 May 2015 14:56:53 +0200 |
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| -1:000000000000 | 0:8f23314345f4 |
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| 1 function H = hilb(n) | |
| 2 %HILB Hilbert matrix. | |
| 3 % HILB(N) is the N-by-N matrix with elements 1/(i+j-1). | |
| 4 % It is a famous example of a badly conditioned matrix. | |
| 5 % COND(HILB(N)) grows like EXP(3.5*N). | |
| 6 % See INVHILB (standard MATLAB routine) for the exact inverse, which | |
| 7 % has integer entries. | |
| 8 % HILB(N) is symmetric positive definite, totally positive, and a | |
| 9 % Hankel matrix. | |
| 10 | |
| 11 % References: | |
| 12 % M.-D. Choi, Tricks or treats with the Hilbert matrix, Amer. Math. | |
| 13 % Monthly, 90 (1983), pp. 301-312. | |
| 14 % N.J. Higham, Accuracy and Stability of Numerical Algorithms, | |
| 15 % Society for Industrial and Applied Mathematics, Philadelphia, PA, | |
| 16 % USA, 1996; sec. 26.1. | |
| 17 % M. Newman and J. Todd, The evaluation of matrix inversion | |
| 18 % programs, J. Soc. Indust. Appl. Math., 6 (1958), pp. 466-476. | |
| 19 % D.E. Knuth, The Art of Computer Programming, | |
| 20 % Volume 1, Fundamental Algorithms, second edition, Addison-Wesley, | |
| 21 % Reading, Massachusetts, 1973, p. 37. | |
| 22 | |
| 23 if n == 1 | |
| 24 H = 1; | |
| 25 else | |
| 26 H = cauchy( (1:n) - .5); | |
| 27 end |