wilkinson

Wilkinson's eigenvalue test matrix

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Syntax

W = wilkinson(n)
W = wilkinson(n,classname)

Description

example

W = wilkinson(n) returns one of J. H. Wilkinson's n-by-n eigenvalue test matrices. W is a symmetric, tridiagonal matrix with pairs of nearly equal eigenvalues.

W = wilkinson(n,classname) returns a matrix of class classname, which can be 'single' or 'double'.

Examples

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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. The eigenvalues agree to 14, but not 15, decimal places.

W = wilkinson(7)
W = 7×7

     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

Input Arguments

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Matrix order, specified as a scalar, nonnegative integer.

Example: wilkinson(10)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char

Matrix class, specified as either 'double' or 'single'.

Example: wilkinson(10,'single')

Data Types: char

Extended Capabilities

See Also

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Introduced before R2006a

MATLAB Documentation

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