Application-tailored linear algebra algorithms

Application-tailored linear algebra algorithms: A search-based approach

In this paper, we tackle the problem of automatically generating algorithms for linear algebra operations by taking advantage of problem-specific knowledge. In most situations, users possess much more information about the problem at hand than what current libraries and computing environments accept; evidence shows that if properly exploited, such information leads to uncommon/unexpected speedu...

Parallel algorithms in linear algebra

This paper provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues, we consider the problem of parallel solution of a nonsingular linear system by Gaussian elimination with partial pivoting. This problem has come to be regarded...

Hardware Tailored Linear Algebra for Implicit Integrators in Embedded NMPC

Nonlinear Model Predictive Control (NMPC) requires the efficient treatment of the dynamic model in the form of a system of continuous-time differential equations. Newtontype optimization relies on a numerical simulation method in addition to the propagation of first or higher order derivatives. In the case of stiff or implicitly defined dynamics, implicit integration schemes are typically prefe...

Linear Algebra Application~ Markov Chains

Fast Algorithms for Linear Algebra Modulo N

Many linear algebra problems over the ring ZZN of integers modulo N can be solved by transforming via elementary row operations an n ⇥ m input matrix A to Howell form H. The nonzero rows of H give a canonical set of generators for the submodule of (ZZN ) m generated by the rows of A. In this paper we present an algorithm to recover H together with an invertible transformation matrix P which sat...