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9 papers · 2 filters
Simultaneous hollowisation, joint numerical range, and stabilization by noise
Tobias Damm, Heike Fassbender
We consider orthogonal transformations of arbitrary square matrices to a form where all diagonal entries are equal. In our main results we treat the simultaneous transformation of…
High Performance Block Incomplete LU Factorization
Matthias Bollhöfer, Olaf Schenk, Fabio Verbosio
Many application problems that lead to solving linear systems make use of preconditioned Krylov subspace solvers to compute their solution. Among the most popular preconditioning a…
Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators
Hendrik Ranocha, Katharina Ostaszewski, Philip Heinisch
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimension…
Shock Capturing by Bernstein Polynomials for Scalar Conservation Laws
Jan Glaubitz
A main disadvantage of many high-order methods for hyperbolic conservation laws lies in the famous Gibbs-Wilbraham phenomenon, once discontinuities appear in the solution. Due to t…
A note on the singular value decomposition of (skew-)involutory and (skew-)coninvolutory matrices
Heike Faßbender, Martin Halwaß
The singular values of an involutory matrix appear in pairs while the singular values may appear in pairs or by themselves.…
Lyapunov and Sylvester equations: A quadrature framework
Christian Bertram, Heike Faßbender
This paper introduces a novel framework for the solution of (large-scale) Lyapunov and Sylvester equations derived from numerical integration methods. Suitable systems of ordinary…