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wilkinson

Wilkinson's eigenvalue test matrix

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

wilkinson(7)

ans = 

    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

The most frequently used case is wilkinson(21). Its two largest eigenvalues are both about 10.746; they agree to 14, but not to 15, decimal places.

See Also

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