Numerical Algorithms and High-Performance Computing - CADMOS Chair

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An Error Analysis Of Galerkin Projection Methods For Linear Systems With Tensor Product Structure

Daniel Kressner, Christine Tobler

Recent results on the convergence of a Galerkin projection method for the Sylvester equation are extended to more general linear systems with tensor product structure. In the Hermitian positive definite case, explicit convergence bounds are derived for Gal ...

Society for Industrial and Applied Mathematics2013

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...

Siam Publications2013

Block-Floating-Point Enhanced MMSE Filter Matrix Computation for MIMO-OFDM Communication Systems

Andreas Peter Burg, Carl Christian Sten Dominic Senning

n this paper we present an architecture for an MMSE ﬁlter matrix computation unit for signal detection in MIMO-OFDM communication systems. We propose to compute the required matrix inverse based on a Cholesky decomposition, followed by a Gauss-Jordan matri ...

2013

The Adomian Decomposition Method for Nonlinear Partial Differential Equations

Natalie Sauerwald

The goal of this report is to study the method introduced by Adomian known as the Adomian Decomposition Method (ADM), which is used to find an approximate solution to nonlinear partial differential equations (PDEs) as a series expansion involving the recur ...

2013

Dynamical Approximation By Hierarchical Tucker And Tensor-Train Tensors

We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch and Lubich; see [SIAM J. Matrix Anal. Appl., 29 (2007), pp. 434-454], [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2360-2375]) to the re ...

Society for Industrial and Applied Mathematics2013

The geometry of algorithms using hierarchical tensors

André Uschmajew

In this paper, the differential geometry of the novel hierarchical Tucker format for tensors is derived. The set HT,k of tensors with fixed tree T and hierarchical rank k is shown to be a smooth quotient manifold, namely the set of orbits of a Lie group ac ...

2013

Structured Canonical Forms For Products Of (Skew-) Symmetric Matrices And The Matrix Equation XAX = B

Daniel Kressner, Xin Liu

The contragredient transformation A bar right arrow P-1 AP-(inverted perpendicular) , B bar right arrow P-inverted perpendicular BP of two matrices A, B effects simultaneous similarity transformations of the products AB and BA. This work provides structure ...

Int Linear Algebra Soc2013

Coupling reduced basis and numerical homogenization methods for solving quasilinear elliptic problems

Assyr Abdulle

The workshop has brought together experts in the broad field of partial differential equations with highly heterogeneous coefficients. Analysts and computational and applied mathematicians have shared results and ideas on a topic of considerable interest b ...

EMS2013

We prove upper bounds for Hecke-Laplace eigenfunctions on certain Riemannian manifolds X of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are d-fold products of 2-spheres or 3-spheres, realiz ...

Cambridge Univ Press2013

Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Sabine Burgdorf

This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of Hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of t ...

Springer2013

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Cambridge Univ Press2013

Hybrid Bounds For Automorphic Forms On Ellipsoids Over Number Fields

Philippe Michel