Historically, iterative solvers have been designed so as to minimize the number of floating-point operations. We propose instead that iterative solvers should be designed to minimize the amount of data that must be loaded from the memory hierarchy to the CPU. In this paper, we describe automated memory analysis, a technique to improve the memory efficiency of a sparse linear iterative solver. O...

Preconditioned iterative solvers have the potential to solve very large sparse linear systems with a fraction of the memory used by direct methods. However, the effectiveness and performance of most preconditioners is not only problem dependent, but also fairly sensitive to the choice of their tunable parameters. As a result, a typical practitioner is faced with an overwhelming number of choice...

This report presents different approaches to solving sparse linear systems—direct and iterative solvers—and compares a number of methods in each category. I also consider the two techniques of using solvers for linear systems: single method solver schemes and multi-method solver schemes. I also present some of the popular systems that use these techniques. This involves surveying the relevant l...

There has been a recent interest in understanding text to perform mathematical reasoning. In particular, most of these efforts have focussed on automatically solving school level math word problems. In order to make advancements in this area accessible to people, as well as to facilitate this line of research, we release the ILLINOIS MATH SOLVER, a web based tool that supports performing mathem...

Historically, iterative solvers have been designed so as to minimize the number of floating-point operations. We propose instead that iterative solvers should be designed to minimize the amount of data that must be loaded from the memory hierarchy to the CPU. In this paper, we describe automated memory analysis, a technique to improve the memory efficiency of a sparse linear iterative solver. O...

The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subset...

In this short paper we present a linear constraint solver for the UniCalc system, an environment for reliable solution of mathematical modeling problems.

This paper presents a class of theoretical and iterative method for linear partial differential equations. An algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. In this technique, the solution is calculated in the form of a series with easily computable components. There test modeling problems from mathematical mechanic, physi...

We present the motivation and results of a benchmarking project for linear solvers employed for semiconductor device and circuit simulation. Based on examples coming from current research projects, the performance of a specific set of linear solvers is evaluated. In rare circumstances the results show that it is important to choose the appropriate type of solver for different kind of simulation...

The technique of iterative reenement for improving the computed solution to a linear system was used on desk calculators and computers in the 1940s and has remained popular. In the 1990s iterative reenement is well supported in software libraries, notably in LAPACK. Although the behaviour of iterative reenement in oating point arithmetic is reasonably well understood, the existing theory is not...