MATLAB Function Reference

hilb

Hilbert matrix

Syntax

H = hilb(n)

Description

H = hilb(n) returns the Hilbert matrix of order n.

Definition

The Hilbert matrix is a notable example of a poorly conditioned matrix [1]. The elements of the Hilbert matrices are: H(i, j) = 1/(i+j-1).

Examples

Even the fourth-order Hilbert matrix shows signs of poor conditioning.

cond(hilb(4)) =
    1.5514e+04

Algorithm

See the M-file for a good example of efficient MATLAB programming where conventional for loops are replaced by vectorized statements.

See Also

invhilb

References

[1] Forsythe, G. E. and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, 1967, Chapter 19.

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