Bibliographic Details
| Title: |
FAST POLYNOMIAL TRANSFORMS BASED ON TOEPLITZ AND HANKEL MATRICES. |
| Authors: |
TOWNSEND, ALEX1 townsend@cornell.edu, WEBB, MARCUS2 marcus.webb@cs.kuleuven.be, OLVER, SHEEHAN s.olver@imperial.ac.uk |
| Source: |
Mathematics of Computation. Jul2018, Vol. 37 Issue 312, p1913-1934. 22p. |
| Subjects: |
Polynomials, Integral transforms, Toeplitz matrices, Hankel functions, Hadamard matrices |
| Abstract: |
Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonallyscaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive algorithms with an observed complexity of O(N log²N), based on the fast Fourier transform, for converting coefficients of a degree N polynomial in one polynomial basis to coefficients in another. Numerical results show that this approach is competitive with state-of-the-art techniques, requires no precomputational cost, can be implemented in a handful of lines of code, and is easily adapted to extended precision arithmetic. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
