wilkinson Matrix

Generate the Wilkinson matrix of size n x n.The Wilkinson matrix for testing eigenvalue computations

wilkinson(n)

Arguments

n

integer

Details

The Wilkinson matrix for testing eigenvalue computations is a symmetric matrix with three non-zero diagonals and with several pairs of nearly equal eigenvalues.

Value

matrix of size n x n

Note

The two largest eigenvalues of wilkinson(21) agree to 14, but not 15 decimal places.

See also

Toeplitz

Examples

(a <- wilkinson(7))
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    3    1    0    0    0    0    0
#> [2,]    1    2    1    0    0    0    0
#> [3,]    0    1    1    1    0    0    0
#> [4,]    0    0    1    0    1    0    0
#> [5,]    0    0    0    1    1    1    0
#> [6,]    0    0    0    0    1    2    1
#> [7,]    0    0    0    0    0    1    3
eig(a)
#> [1]  3.7615572  3.7320508  2.3633282  2.0000000  1.0000000  0.2679492 -1.1248854