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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On computations with dense structured matrices
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by Victor Pan PDF
Math. Comp. 55 (1990), 179-190 Request permission

Abstract:

We reduce several computations with Hilbert and Vandermonde type matrices to matrix computations of the Hankel-Toeplitz type (and vice versa). This unifies various known algorithms for computations with dense structured matrices and enables us to extend any progress in computations with matrices of one class to the computations with other classes of matrices. In particular, this enables us to compute the inverses and the determinants of $n \times n$ matrices of Vandermonde and Hilbert types for the cost of $O(n{\log ^2}n)$ arithmetic operations. (Previously, such results were only known for the more narrow class of Vandermonde and generalized Hilbert matrices.)
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 55 (1990), 179-190
  • MSC: Primary 65F30
  • DOI: https://doi.org/10.1090/S0025-5718-1990-1023051-7
  • MathSciNet review: 1023051