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annotate toolbox/lehmer.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +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 = lehmer(n)
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Antonio Pino Robles <data.script93@gmail.com>
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2 %LEHMER Lehmer matrix - symmetric positive definite.
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Antonio Pino Robles <data.script93@gmail.com>
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3 % A = LEHMER(N) is the symmetric positive definite N-by-N matrix with
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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4 % A(i,j) = i/j for j >= i.
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Antonio Pino Robles <data.script93@gmail.com>
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5 % A is totally nonnegative. INV(A) is tridiagonal, and explicit
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Antonio Pino Robles <data.script93@gmail.com>
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6 % formulas are known for its entries.
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7 % N <= COND(A) <= 4*N*N.
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9 % References:
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10 % M. Newman and J. Todd, The evaluation of matrix inversion
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11 % programs, J. Soc. Indust. Appl. Math., 6 (1958), pp. 466-476.
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12 % Solutions to problem E710 (proposed by D.H. Lehmer): The inverse
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13 % of a matrix, Amer. Math. Monthly, 53 (1946), pp. 534-535.
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14 % J. Todd, Basic Numerical Mathematics, Vol. 2: Numerical Algebra,
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15 % Birkhauser, Basel, and Academic Press, New York, 1977, p. 154.
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16
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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17 A = ones(n,1)*(1:n);
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18 A = A./A';
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19 A = tril(A) + tril(A,-1)';