12 citations · 19 across the 11 of their papers we have counts for
14 papers
Updating and Downdating the Recurrences of Discrete Multiple Orthogonal Polynomials on the Real Line
Amin Faghih, Marc Van Barel, Raf Vandebril
We study multiple orthogonal polynomials with orthogonality defined by multiple positive discrete measures on the real line. Focusing on type~I and type~II multiple orthogonal poly…
An Arnoldi-based approach to polynomial and rational least squares problems
Amin Faghih, Marc Van Barel, Niel Van Buggenhout +1
In this research, we solve polynomial, Sobolev polynomial, rational, and Sobolev rational least squares problems. Although the increase in the approximation degree allows us to fit…
Generalized cyclic symmetric decompositions for the matrix multiplication tensor
Charlotte Vermeylen, Marc Van Barel
A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to…
A Riemannian rank-adaptive method for higher-order tensor completion in the tensor-train format
Charlotte Vermeylen, Marc Van Barel
In this paper a new Riemannian rank adaptive method (RRAM) is proposed for the low-rank tensor completion problem (LRTCP) formulated as a least-squares optimization problem on the…
Stability Improvements for Fast Matrix Multiplication
Charlotte Vermeylen, Marc Van Barel
We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find polyadic decompositions of the matrix multiplication tensor. We u…
Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format
Charlotte Vermeylen, Guillaume Olikier, P. -A. Absil +1
We propose a numerical method to obtain an adequate value for the upper bound on the rank for the tensor completion problem on the variety of third-order tensors of bounded tensor-…
A generalization of Floater--Hormann interpolants
Woula Themistoclakis, Marc Van Barel
In this paper the interpolating rational functions introduced by Floater and Hormann are generalized leading to a whole new family of rational functions depending on , an additi…
An Approximate Projection onto the Tangent Cone to the Variety of Third-Order Tensors of Bounded Tensor-Train Rank
Charlotte Vermeylen, Guillaume Olikier, Marc Van Barel
An approximate projection onto the tangent cone to the variety of third-order tensors of bounded tensor-train rank is proposed and proven to satisfy a better angle condition than t…
Algorithms for Modifying Recurrence Relations of Orthogonal Polynomial and Rational Functions when Changing the Discrete Inner Product
Marc Van Barel, Niel Van Buggenhout, Raf Vandebril
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instea…
Equivalent Polyadic Decompositions of Matrix Multiplication Tensors
Guillaume O. Berger, P. -A. Absil, Lieven De Lathauwer +2
Invariance transformations of polyadic decompositions of matrix multiplication tensors define an equivalence relation on the set of such decompositions. In this paper, we present a…
Optimal Lebesgue constants for least squares polynomial approximation on the (hyper)sphere
Woula Themistoclakis, Marc Van Barel
We investigate the uniform approximation provided by least squares polynomials on the unit Euclidean sphere in , with . Like any other poly…
Uniform approximation on the sphere by least squares polynomials
Woula Themistoclakis, Marc Van Barel
The paper concerns the uniform polynomial approximation of a function , continuous on the unit Euclidean sphere of and known only at a finite number of points th…
Truncated Normal Forms for Solving Polynomial Systems: Generalized and Efficient Algorithms
Bernard Mourrain, Simon Telen, Marc Van Barel
We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. Normal form alg…
A Stabilized Normal Form Algorithm for Generic Systems of Polynomial Equations
Simon Telen, Marc Van Barel
We propose a numerical linear algebra based method to find the multiplication operators of the quotient ring associated to a zero-dimensional ideal generated…