Inverse of Hilbert matrix
H = invhilb(n)
H = invhilb(n,classname)
H = invhilb( generates the exact
inverse of the exact Hilbert matrix for
n less than about 15. For
invhilb function generates an
approximation to the inverse Hilbert matrix.
Compute the fourth-order inverse Hilbert matrix.
ans = 4×4 16 -120 240 -140 -120 1200 -2700 1680 240 -2700 6480 -4200 -140 1680 -4200 2800
n— Matrix order
Matrix order, specified as a scalar, nonnegative integer.
classname— Matrix class
Matrix class, specified as either
The exact inverse of the exact Hilbert matrix is a matrix whose elements are large
integers. As long as the order of the matrix
n is less than 15, these
integers can be represented as floating-point numbers without roundoff error.
the effects of two or three sets of roundoff errors:
Errors caused by representing
Errors in the matrix inversion process
Errors, if any, in representing
The first of these roundoff errors involves representing fractions like 1/3 and 1/5 in floating-point representation and is the most significant.
 Forsythe, G. E. and C. B. Moler. Computer Solution of Linear Algebraic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1967.