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annotate toolbox/neumann.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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1 function [A, T] = neumann(n)
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2 %NEUMANN Singular matrix from the discrete Neumann problem (sparse).
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3 % NEUMANN(N) is the singular, row diagonally dominant matrix resulting
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4 % from discretizing the Neumann problem with the usual five point
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5 % operator on a regular mesh.
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6 % It has a one-dimensional null space with null vector ONES(N,1).
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7 % The dimension N should be a perfect square, or else a 2-vector,
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8 % in which case the dimension of the matrix is N(1)*N(2).
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10 % Reference:
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11 % R.J. Plemmons, Regular splittings and the discrete Neumann
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12 % problem, Numer. Math., 25 (1976), pp. 153-161.
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14 if max(size(n)) == 1
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15 m = sqrt(n);
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16 if m^2 ~= n, error('N must be a perfect square.'), end
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17 n(1) = m; n(2) = m;
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18 end
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19
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20 T = tridiag(n(1), -1, 2, -1);
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21 T(1,2) = -2;
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22 T(n(1),n(1)-1) = -2;
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23
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24 A = kron(T, eye(n(2))) + kron(eye(n(2)), T);