Zobrazeno 1 - 10
of 382
pro vyhledávání: '"Van Barel, Marc"'
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 the data better in attacking least squares problems, the ill-conditio
Externí odkaz:
http://arxiv.org/abs/2407.05945
Autor:
Vermeylen, Charlotte, Van Barel, Marc
In this paper we propose a new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication to reduce the number of variables in the optimization proble
Externí odkaz:
http://arxiv.org/abs/2404.16699
Autor:
Vermeylen, Charlotte, Van Barel, Marc
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 algebraic variety of tensors of bounded tensor-train (TT) rank. The me
Externí odkaz:
http://arxiv.org/abs/2402.12182
Autor:
Vermeylen, Charlotte, Van Barel, Marc
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 use this method to obtain new discrete decompositions and parameter fam
Externí odkaz:
http://arxiv.org/abs/2310.02794
Publikováno v:
2023 31st European Signal Processing Conference (EUSIPCO)
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-train rank. The method is inspired by the parametrization of the tange
Externí odkaz:
http://arxiv.org/abs/2309.15170
Autor:
Themistoclakis, Woula, Van Barel, Marc
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 $\gamma$, an additional positive integer parameter. For $\gamma = 1$, the original F
Externí odkaz:
http://arxiv.org/abs/2307.05345
Publikováno v:
Geometric Science of Information 2023. Lecture Notes in Computer Science, vol 14071. Springer, 484-493
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 the one proposed by Kutschan (2019). Such an approximate projection ena
Externí odkaz:
http://arxiv.org/abs/2306.13360
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed. Moreover, also typ
Externí odkaz:
http://arxiv.org/abs/2302.00355
Many problems in Science and Engineering give rise to linear integral equations of the first kind with a smooth kernel. Discretization of the integral operator yields a matrix, whose singular values cluster at the origin. We describe the approximatio
Externí odkaz:
http://arxiv.org/abs/2204.05740
Publikováno v:
In Applied Numerical Mathematics June 2024 200:429-452
