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Subject Item
dbr:Hilbert_matrix
rdfs:label
Hilbert matrix
rdfs:comment
In linear algebra, a Hilbert matrix, introduced by Hilbert, is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: The Hilbert matrix can be regarded as derived from the integral that is, as a Gramian matrix for powers of x. It arises in the least squares approximation of arbitrary functions by polynomials. The Hilbert matrices are canonical examples of ill-conditioned matrices, being notoriously difficult to use in numerical computation. For example, the 2-norm condition number of the matrix above is about 4.8×105.
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dbo:abstract
In linear algebra, a Hilbert matrix, introduced by Hilbert, is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: The Hilbert matrix can be regarded as derived from the integral that is, as a Gramian matrix for powers of x. It arises in the least squares approximation of arbitrary functions by polynomials. The Hilbert matrices are canonical examples of ill-conditioned matrices, being notoriously difficult to use in numerical computation. For example, the 2-norm condition number of the matrix above is about 4.8×105.
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n11:Hilbert_matrix