Publications related to Tensor product of fields

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

Jonathan Gruber

Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...

EPFL2022

TCB-spline-based isogeometric analysis method with high-quality parameterizations

Xiaodong Wei, Juan Cao

Isogeometric analysis (IGA) was introduced to integrate methods for analysis and computer-aided design (CAD) into a unified process. High-quality parameterization of a physical domain plays a crucial role in IGA. However, obtaining high-quality parameteriz ...

ELSEVIER SCIENCE SA2022

Functional Tucker Approximation Using Chebyshev Interpolation

Daniel Kressner, Christoph Max Strössner

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function approximations tha ...

SIAM PUBLICATIONS2021

Gaussian Mixture Regression on Symmetric Positive Definite Matrices Manifolds: Application to Wrist Motion Estimation with sEMG

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

In many sensing and control applications, data are represented in the form of symmetric positive definite (SPD) matrices. Considering the underlying geometry of this data space can be beneficial in many robotics applications. In this paper, we present an e ...

2017

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For~

q

a prime power, the discrete logarithm problem (DLP) in~

\F_{q}

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer~

x

such that

g^x = h

. We present an algorithm for computing discrete logarithm ...

2016

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

Siam Publications2016

Inhomogeneous minima of mixed signature lattices

Eva Bayer Fluckiger, Martino Borello, Peter Simon Jossen

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Academic Press Inc Elsevier Science2016

On the discrete logarithm problem in finite fields of fixed characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For

q

a prime power, the discrete logarithm problem (DLP) in

\mathbb{F}_q

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer

x

such that

g^x = h

. We present an algorithm for computing discrete log ...

2015

Tensor product of fields

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Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Low-Rank Tensor Methods for High-Dimensional Problems

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

TCB-spline-based isogeometric analysis method with high-quality parameterizations

Functional Tucker Approximation Using Chebyshev Interpolation

Gaussian Mixture Regression on Symmetric Positive Definite Matrices Manifolds: Application to Wrist Motion Estimation with sEMG

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Inhomogeneous minima of mixed signature lattices

On the discrete logarithm problem in finite fields of fixed characteristic

Low-Rank Tensor Methods for High-Dimensional Problems

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Gaussian Mixture Regression on Symmetric Positive Definite Matrices Manifolds: Application to Wrist Motion Estimation with sEMG

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

TCB-spline-based isogeometric analysis method with high-quality parameterizations

Functional Tucker Approximation Using Chebyshev Interpolation

On the discrete logarithm problem in finite fields of fixed characteristic

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

Inhomogeneous minima of mixed signature lattices