wilkinson

Wilkinson's eigenvalue test matrix

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Syntax

W = wilkinson(n)

Description

W = wilkinson(n) returns one of J. H. Wilkinson's eigenvalue test matrices. It is a symmetric, tridiagonal matrix with pairs of nearly, but not exactly, equal eigenvalues.

Examples

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Open Script

Compute a 7-by-7 Wilkinson eigenvalue test matrix. The most frequently used case is wilkinson(21), whose two largest eigenvalues are approximately 10.746; they agree to 14, but not 15, decimal places.

W = wilkinson(7)

W =

     3     1     0     0     0     0     0
     1     2     1     0     0     0     0
     0     1     1     1     0     0     0
     0     0     1     0     1     0     0
     0     0     0     1     1     1     0
     0     0     0     0     1     2     1
     0     0     0     0     0     1     3

See Also

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Introduced before R2006a

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