The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision ...

We propose a general algorithm for solving an $n\times n$ nonsingular linear system $Ax = b$ based on iterative refinement with three precisions. The working precision is combined with possibly different precisions for solving for the correction term and for ...

Iterative refinement is a long-standing technique for improving the accuracy of a computed solution to a nonsingular linear system $Ax = b$ obtained via LU factorization. It makes use of residuals computed in extra precision, typically at twice the working ...

We propose a scheme for reduced-precision representation of floating point data on a continuum between IEEE-754 floating point types. Our scheme enables the use of lower precision formats for a reduction in storage space requirements and data transfer ...

The worst-case peak gain (WCPG) of a linear filter is an important measure for the implementation of signal processing algorithms. It is used in the error propagation analysis for filters, thus a reliable evaluation with controlled precision is ...

We have implemented a fast double-double precision (has approx. 32 decimal significant digits) version of matrix-matrix multiplication routine called gRgemm h of MPACK (http://mplapack.sourceforge.net/) on NVIDIA C2050 GPU. This routine is a higher ...

We are interested in the accuracy of linear algebra operations; accuracy of the solution of linear equation, eigenvalue and eigenvectors of some matrices, etc. This is a reason for we have been developing the MPACK. The MPACK consists of MBLAS and ...

The rapid evolution of reconfigurable computing places a great demand for Floating Point Multipliers (FPMs) capable of supporting wide range of application domains from scientific computing to multimedia applications. While former needs the support of ...

The evaluation of special functions often involves the evaluation of numerical constants. When the precision of the evaluation is known in advance (e.g., when developing libms) these constants are simply precomputed once and for all. In contrast, when ...

This article describes a collection of Fortran-95 routines for evaluating the exponential integral function, error function, sine and cosine integrals, Fresnel integrals, Bessel functions, and related mathematical special functions using the FM multiple-...

This article presents a portable C++ system for multiple precision calculations of special functions called e_float. It has an extendable architecture with a uniform C++ layer which can be used with any suitably prepared MP type. The system implements ...

A so called staggered precision arithmetic is a special kind of a multiple precision arithmetic based on the underlying floating point data format (typically IEEE double format) and fast floating point operations as well as exact dot product ...

We apply an iterative refinement method based on a linear Newton iteration to solve a particular group of high precision computation problems. The method generates an initial solution at hardware floating point precision using a traditional method and ...

A collection of Fortran-90 routines for evaluating the gamma function and related functions using the FM multiple-precision arithmetic package.

This article describes a collection of Fortran routines for multiple-precision complex arithmetic and elementary functions. The package provides good exception handling, flexible input and output, trace features, and results that are almost always ...

A minimum-knowledge scheme allows a claimant to prove its identity to a verifier without disclosing any secret information. Minimum-knowledge schemes, incorporating identity verification, signature generation and verification, are generally based on ...

A description is given of a program for computing the solution to a small number of standard numerical analysis problems to any specified accuracy, up to a limit of 2000 correct decimal places. Each computed number is bounded in an interval with a ...