Manfred R. Trummer
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View article: Numerical stability of structure-preserving direct solvers for centrosymmetric linear systems
Numerical stability of structure-preserving direct solvers for centrosymmetric linear systems Open
This paper analyzes direct solvers for centrosymmetric linear systems by applying structure-preserving factorizations with a particular focus on assessing their stability. We build on existing algorithms and complement the factorizations w…
View article: On the invertibility of matrices with a double saddle-point structure
On the invertibility of matrices with a double saddle-point structure Open
We establish necessary and sufficient conditions for invertibility of symmetric three-by-three block matrices having a double saddle-point structure that guarantee the unique solvability of double saddle-point systems. We consider various …
View article: On the invertibility of matrices with a double saddle-point structure
On the invertibility of matrices with a double saddle-point structure Open
We establish necessary and sufficient conditions for invertibility of symmetric three-by-three block matrices having a double saddle-point structure \fb{that guarantee the unique solvability of double saddle-point systems}. We consider var…
View article: Extrapolation quadrature from equispaced samples of functions with jumps
Extrapolation quadrature from equispaced samples of functions with jumps Open
Based on the Euler–Maclaurin formula, the Romberg quadrature method extrapolates trapezoidal values to improve their accuracy when computing the integral of smooth functions from equispaced samples. It has been known at least since an arti…
View article: A Spectral Collocation Method for Systems of Singularly Perturbed Boundary Value Problems
A Spectral Collocation Method for Systems of Singularly Perturbed Boundary Value Problems Open
We present a spectrally accurate method for solving coupled singularly perturbed second order two-point boundary value problems (BVPs). The method combines analytical coordinate transformations with a standard Chebyshev spectral collocatio…