Name
Abstract | ||
|---|---|---|
The polynomial interpolation problem with distinct interpolation points and the polynomial represented in the power basis gives rise to a linear system of equations with a Vandermonde matrix. This system can be solved efficiently by exploiting the structure of the Vandermonde matrix with the aid of the Björck–Peyrera algorithm. We are concerned with polynomial least-squares approximation at the zeros of Chebyshev polynomials. This gives rise to a rectangular Vandermonde matrix. We describe fast algorithms for the factorization of these matrices. Both QR and QR-like factorizations are discussed. The situations when the nodes are extreme points of Chebyshev polynomials or zeros of some classical orthogonal polynomial also are considered. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s11075-018-0560-9 | Numerical Algorithms |
Keywords | Field | DocType |
Vandermonde matrix, Fast factorization, Chebyshev nodes | Chebyshev nodes,Chebyshev polynomials,Applied mathematics,Orthogonal polynomials,Polynomial interpolation,Polynomial,Matrix (mathematics),Mathematical analysis,Interpolation,Vandermonde matrix,Mathematics | Journal |
Volume | Issue | ISSN |
81.0 | 2 | 1572-9265 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mykhailo Kuian | 1 | 0 | 0.34 |
| Lothar Reichel | 2 | 453 | 95.02 |
| Sergij V. Shiyanovskii | 3 | 0 | 0.68 |