Add to ORKGVandermonde matrices are exponentially ill-conditioned, rendering the familiar “polyval(polyfit)” algorithm for polynomial interpolation and least-squares fitting ineffective at higher degrees. We show that Arnoldi orthogonalization fixes the problem. This amounts to on-the-fly construction of discrete orthogonal polynomials by Stieltjes orthogonalization
Univariate and multivariate polynomials play a fundamental role in pure and applied mathematics. In ...
We provide a robust and general algorithm for computing distribution functions associated to induced...
AbstractRelations between rational interpolants and Hankel matrices are investigated. A modification...
AbstractWe present a new O(n3) algorithm for computing the SVD of an n×n polynomial Vandermonde matr...
AbstractThe condition number (relative to the Frobenius norm) of the n × n matrix Pn = [pi−1(xj)]i, ...
AbstractThe condition number (relative to the Frobenius norm) of the n × n matrix Pn = [pi−1(xj)]i, ...
Fast orthogonalization schemes for m\times n Vandermonde matrices V=(z_i^j), introduced by Demeure...
In this note, we extend the Vandermonde with Arnoldi method recently advocated by P. D. Brubeck, Y. ...
AbstractIn this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear syst...
The Vandermonde matrix naturally appears in systems of equations for applications of polynomial appr...
The Vandermonde matrix naturally appears in systems of equations for applications of polynomial appr...
AbstractWe present a new O(n3) algorithm for computing the SVD of an n×n polynomial Vandermonde matr...
Multipoint polynomial evaluation and interpolation are fundamental for modern algebraic and numerica...
Discrete orthogonal matrices have applications in information coding and cryptography. It is often c...
We provide a robust and general algorithm for computing distribution functions associated to induced...
Univariate and multivariate polynomials play a fundamental role in pure and applied mathematics. In ...
We provide a robust and general algorithm for computing distribution functions associated to induced...
AbstractRelations between rational interpolants and Hankel matrices are investigated. A modification...
AbstractWe present a new O(n3) algorithm for computing the SVD of an n×n polynomial Vandermonde matr...
AbstractThe condition number (relative to the Frobenius norm) of the n × n matrix Pn = [pi−1(xj)]i, ...
AbstractThe condition number (relative to the Frobenius norm) of the n × n matrix Pn = [pi−1(xj)]i, ...
Fast orthogonalization schemes for m\times n Vandermonde matrices V=(z_i^j), introduced by Demeure...
In this note, we extend the Vandermonde with Arnoldi method recently advocated by P. D. Brubeck, Y. ...
AbstractIn this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear syst...
The Vandermonde matrix naturally appears in systems of equations for applications of polynomial appr...
The Vandermonde matrix naturally appears in systems of equations for applications of polynomial appr...
AbstractWe present a new O(n3) algorithm for computing the SVD of an n×n polynomial Vandermonde matr...
Multipoint polynomial evaluation and interpolation are fundamental for modern algebraic and numerica...
Discrete orthogonal matrices have applications in information coding and cryptography. It is often c...
We provide a robust and general algorithm for computing distribution functions associated to induced...
Univariate and multivariate polynomials play a fundamental role in pure and applied mathematics. In ...
We provide a robust and general algorithm for computing distribution functions associated to induced...
AbstractRelations between rational interpolants and Hankel matrices are investigated. A modification...