9 citations · 17 across the 20 of their papers we have counts for
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Review of Cyclic Reduction for Parallel Solution of Hermitian Positive Definite Block-Tridiagonal Linear Systems
Martin Neuenhofen
Cyclic reduction is a method for the solution of (block-)tridiagonal linear systems. In this note we review the method tailored to hermitian positive definite banded linear systems…
Determination of Positive Definiteness through Shift-and-Invert Iteration in Weakly Polynomial Complexity
Martin Neuenhofen
We propose a numerical method, based on the shift-and-invert power iteration, that answers whether a symmetric matrix is positive definite ("yes") or not ("no"). Our method uses ra…
Note on the Modifed Augmented Lagrangian Method for Minimization of Functions with Large Quadratic Penalties
Martin Neuenhofen
In a recent work (arXiv-DOI: 1804.08072v1) we introduced the Modified Augmented Lagrangian Method (MALM) for the efficient minimization of objective functions with large quadratic…
Weakly polynomial efficient minimization of a non-convex quadratic function with logarithmic barriers in a trust-region
Martin Neuenhofen
We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a -trust-region (i.e. cub…
Interior Point Method with Modified Augmented Lagrangian for Penalty-Barrier Nonlinear Programming
Martin Neuenhofen
We present a numerical method for the local solution of nonlinear programming problems. The SUMT approach of Fiacco and McCormick results in a merit function with quadratic penalti…
Modified Augmented Lagrangian Method for the minimization of functions with quadratic penalty terms
Martin Neuenhofen
The Augmented Lagrangian Method (ALM) is an iterative method for the solution of equality-constrained non-linear programming problems. In contrast to the quadratic penalty method,…
PPD-IPM: Outer primal, inner primal-dual interior-point method for nonlinear programming
Martin Neuenhofen
In this paper we present a novel numerical method for computing local minimizers of twice smooth differentiable non-linear programming (NLP) problems. So far all algorithms for NLP…
A time-optimal algorithm for solving (block-)tridiagonal linear systems of dimension N on a distributed computer of N nodes
Martin Neuenhofen
We are concerned with the fastest possible direct numerical solution algorithm for a thin-banded or tridiagonal linear system of dimension on a distributed computing network of…
High-order convergent Finite-Elements Direct Transcription Method for Constrained Optimal Control Problems
Martin Peter Neuenhofen
In this paper we present a finite element method for the direct transcription of constrained non-linear optimal control problems. We prove that our method converges of high order u…
A restarted GMRES-based implementation of IDR(s)stab(L) to yield higher robustness
Martin P. Neuenhofen
In this thesis we propose a novel implementation of IDRstab that avoids several unlucky breakdowns of current IDRstab implementations and is further capable of benefiting from a pa…
M(s)stab(L): A Generalization of IDR(s)stab(L) for Sequences of Linear Systems
Martin Peter Neuenhofen
We propose Mstab, a novel Krylov subspace recycling method for the iterative solution of sequences of linear systems with fixed system matrix and changing right-hand sides. This ne…
Memory-efficient recycling of large Krylov-subspaces for sequences of Hermitian linear systems
Martin Peter Neuenhofen, Sven Groß
We present a new short-recurrence reaidual-optimal Krylov subspace recycling method for sequences of Hermitian systems of linear equations with a fixed system matrix and changing r…
Short-Recurrence and -Storage Recycling of large Krylov-Subspaces for Sequences of Linear Systems with changing Right-Hand-Sides
Martin Neuenhofen
In this text I present a couple of new principles and thereon based iterative methods for numerical solution of sequences of systems of linear equations with fixed system matrix an…