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hilb
Hilbert matrix
H = hilb(n)
H = hilb(n)
returns the Hilbert matrix of order n.
The Hilbert matrix is a notable example of a poorly conditioned matrix [1]. The elements of the Hilbert matrices are
.
Even the fourth-order Hilbert matrix shows signs of poor conditioning.
cond(hilb(4)) =
1.5514e+04
See the M-file for a good example of efficient MATLAB programming where conventional for loops are replaced by vectorized statements.
invhilb Inverse of the Hilbert matrix
[1] Forsythe, G. E. and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, 1967, Chapter 19.