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Makematrix >> Makematrix > makematrix_gallery

makematrix_gallery

Test matrices

Calling Sequence

A = makematrix_gallery(3)
A = makematrix_gallery(4)
A = makematrix_gallery(5)
A = makematrix_gallery(8)
A = makematrix_gallery("cauchy",x)
A = makematrix_gallery("cauchy",x,y)
A = makematrix_gallery("circul",x)

Parameters

x :

a 1-by-n or n-by-1 matrix of doubles, the x input

y :

a 1-by-n or n-by-1 matrix of doubles, the y input

A :

a n-by-n matrix of doubles, the matrix

Description

makematrix_gallery(3) is a badly conditioned 3-by-3 matrix.

makematrix_gallery(4) is the Wilson matrix. It is symmetric positive definite, integer inverse.

makematrix_gallery(5) is an interesting eigenvalue problem.

makematrix_gallery(8) is a ill-conditionned matrix. Exact eigenvalues from Westlake (1968), p.150 are:

a = sqrt(10405);
b = sqrt(26);
e = [-10*a,   0,   510-100*b,  1000,   1000,   510+100*b, 1020,   10*a]';

makematrix_gallery("cauchy",x) is the Cauchy matrix, where y is set to x (see makematrix_cauchy).

makematrix_gallery("cauchy",x,y) is the Cauchy matrix (see makematrix_cauchy).

makematrix_gallery("circul",x) is the circular matrix (see makematrix_circul).

Examples

A = makematrix_gallery(3)
cond(makematrix_gallery(3))

A = makematrix_gallery(4)

A = makematrix_gallery(5)

A = makematrix_gallery(8)
cond(makematrix_gallery(8))

A = makematrix_gallery("cauchy" , 1:5 )

A = makematrix_gallery("circul" , 1:5 )

Authors

Bibliography

J.R. Westlake, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations, John Wiley, New York, 1968.

J.H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, 1965.

"The Test Matrix Toolbox for Matlab (Version 3.0)", Nicolas Higham, Numerical Analysis Report No. 276, September 1995, Manchester Centre for Computational Mathematics, The University of Manchester

"Algorithm 694: a collection of test matrices in MATLAB", Nicolas Higham, ACM Transactions on Mathematical Software, Volume 17 , Issue 3 (September 1991), Pages: 289 - 305

"Higham's Test Matrices ", John Burkardt, 2005, http://people.sc.fsu.edu/~burkardt/m_src/test_matrix/test_matrix.html

"A Handbook of Numerical Matrix Inversion and Solution of Linear Equations", J.R. Westlake, John Wiley, New York, 1968.

"The Algebraic Eigenvalue Problem", J.H. Wilkinson, Oxford University Press, 1965.


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