Jacko Koster

Bio: Jacko Koster is an academic researcher from University of Bergen. The author has contributed to research in topics: Solver & Sparse matrix. The author has an hindex of 10, co-authored 12 publications receiving 2955 citations.

A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling

Abstract: In this paper, we analyze the main features and discuss the tuning of the algorithms for the direct solution of sparse linear systems on distributed memory computers developed in the context of a long term European research project. The algorithms use a multifrontal approach and are especially designed to cover a large class of problems. The problems can be symmetric positive definite, general symmetric, or unsymmetric matrices, both possibly rank deficient, and they can be provided by the user in several formats. The algorithms achieve high performance by exploiting parallelism coming from the sparsity in the problem and that available for dense matrices. The algorithms use a dynamic distributed task scheduling technique to accommodate numerical pivoting and to allow the migration of computational tasks to lightly loaded processors. Large computational tasks are divided into subtasks to enhance parallelism. Asynchronous communication is used throughout the solution process to efficiently overlap communication with computation. We illustrate our design choices by experimental results obtained on an SGI Origin 2000 and an IBM SP2 for test matrices provided by industrial partners in the PARASOL project.

On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix

Abstract: We consider bipartite matching algorithms for computing permutations of a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various strategies for this and consider their implementation as computer codes. We also consider scaling techniques to further increase the relative values of the diagonal entries. Numerical experiments show the effect of the reorderings and the scaling on the solution of sparse equations by a direct method and by preconditioned iterative techniques.

On algorithms for permuting large entries to the diagonal of a sparse matrix

Abstract: We consider bipartite matching algorithms for computing permutations of a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various strategies for this and consider their implementation as computer codes. We also consider scaling techniques to further increase the relative values of the diagonal entries. Numerical experiments show the effect of the reorderings and the scaling on the solution of sparse equations by a direct method and by preconditioned iterative techniques.

The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices

Abstract: We consider techniques for permuting a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various criteria for this and consider their implementation as computer codes. We then indicate several cases where such a permutation can be useful. These include the solution of sparse equations by a direct method and by an iterative technique. We also consider its use in generating a preconditioner for an iterative method. We see that the effect of these reorderings can be dramatic although the best a priori strategy is by no means clear.

The design and use of algorithms for permuting large entries to the diagonal of sparse matrices

Abstract: We consider techniques for permuting a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various criteria for this and consider their implementation as computer codes. We then indicate several cases where such a permutation can be useful. These include the solution of sparse equations by a direct method and by an iterative technique. We also consider its use in generating a preconditioner for an iterative method. We see that the effect of these reorderings can be dramatic although the best a priori strategy is by no means clear.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

The university of Florida sparse matrix collection

Abstract: We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs) We provide software for accessing and managing the Collection, from MATLAB™, Mathematica™, Fortran, and C, as well as an online search capability Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task

Numerical solution of saddle point problems

Abstract: Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling

Abstract: In this paper, we analyze the main features and discuss the tuning of the algorithms for the direct solution of sparse linear systems on distributed memory computers developed in the context of a long term European research project. The algorithms use a multifrontal approach and are especially designed to cover a large class of problems. The problems can be symmetric positive definite, general symmetric, or unsymmetric matrices, both possibly rank deficient, and they can be provided by the user in several formats. The algorithms achieve high performance by exploiting parallelism coming from the sparsity in the problem and that available for dense matrices. The algorithms use a dynamic distributed task scheduling technique to accommodate numerical pivoting and to allow the migration of computational tasks to lightly loaded processors. Large computational tasks are divided into subtasks to enhance parallelism. Asynchronous communication is used throughout the solution process to efficiently overlap communication with computation. We illustrate our design choices by experimental results obtained on an SGI Origin 2000 and an IBM SP2 for test matrices provided by industrial partners in the PARASOL project.