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makematrix_wilkinsonp

Returns the Wilkinson + matrix

Calling Sequence

A = makematrix_wilkinsonp ( n )

Parameters

n :

a 1-by-1 matrix of doubles, integer value, the size of the matrix to return

A :

a n-by-n matrix of doubles, integer values

Description

"The W+matrix (Wilkinson 1965, p 308) is normally given odd order. This tridiagonal matrix then has several pairs of close eigenvalues despite the fact that no superdiagonal element is small. Wilkinson points out that the separation between the two largest eigenvalues is of the order of (n!)-2 so that the power method will be unable to separate them unless n is very small."

Examples

A = makematrix_wilkinsonp ( 5 )

Authors

Bibliography

J.C. Nash, Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, second edition, Adam Hilger, Bristol, 1990 (Appendix 1).

J.H. Wilkinson, The Algebraic Eigenvalue Problem, p. 308, "Close eigenvalues and small beta", W5+


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