Inverse of the Hilbert matrix
Syntax
H = invhilb(n)
Description
H = invhilb(n)
generates the exact inverse of the exact Hilbert matrix for n less than about 15. For larger n, invhilb(n) generates an approximation to the inverse Hilbert matrix.
Limitations
The exact inverse of the exact Hilbert matrix is a matrix whose elements are large integers. These integers may be represented as floating-point numbers without roundoff error as long as the order of the matrix, n, is less than 15.
Comparing invhilb(n) with inv(hilb(n)) involves the effects of two or three sets of roundoff errors:
It turns out that the first of these, which involves representing fractions like 1/3 and 1/5 in floating-point, is the most significant.
Examples
invhilb(4) is
16 -120 240 -140
-120 1200 -2700 1680
240 -2700 6480 -4200
-140 1680 -4200 2800
See Also
hilb Hilbert matrix
References
[1] Forsythe, G. E. and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, 1967, Chapter 19.
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