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invhilb
Inverse of the Hilbert matrix
H = invhilb(n)
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.
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:
hilb(n)
invhilb(n)
invhilb(4)
is
16 -120 240 -140 -120 1200 -2700 1680 240 -2700 6480 -4200 -140 1680 -4200 2800
hilb
Hilbert matrix
[1] Forsythe, G. E. and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, 1967, Chapter 19.