Fast algorithms using orthogonal polynomials
| Autor: | Alex Townsend, Richard Mikael Slevinsky, Sheehan Olver |
|---|---|
| Přispěvatelé: | The Leverhulme Trust |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Rank (linear algebra) Computer science Differential equation General Mathematics 0103 Numerical and Computational Mathematics MathematicsofComputing_NUMERICALANALYSIS Spherical harmonics Numerical & Computational Mathematics 010103 numerical & computational mathematics Singular integral 01 natural sciences Quadrature (mathematics) 010101 applied mathematics Orthogonality 0102 Applied Mathematics Linear algebra Orthogonal polynomials ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0101 mathematics Algorithm |
| Popis: | We review recent advances in algorithms for quadrature, transforms, differential equations and singular integral equations using orthogonal polynomials. Quadrature based on asymptotics has facilitated optimal complexity quadrature rules, allowing for efficient computation of quadrature rules with millions of nodes. Transforms based on rank structures in change-of-basis operators allow for quasi-optimal complexity, including in multivariate settings such as on triangles and for spherical harmonics. Ordinary and partial differential equations can be solved via sparse linear algebra when set up using orthogonal polynomials as a basis, provided that care is taken with the weights of orthogonality. A similar idea, together with low-rank approximation, gives an efficient method for solving singular integral equations. These techniques can be combined to produce high-performance codes for a wide range of problems that appear in applications. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|