Parallel Software to Offset the Cost of Higher Precision

TL;DR

This paper presents a parallel software approach to offset the computational overhead of higher-precision arithmetic in scientific computing, demonstrated through Newton's method for algebraic space curves.

Contribution

It introduces a parallel algorithm that mitigates the cost of software-based high-precision calculations in scientific applications.

Findings

Parallel algorithms effectively reduce overhead of high-precision computations

Newton's method applied to algebraic space curves demonstrates the approach

Significant performance improvements observed in experimental results

Abstract

Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates for this overhead. Newton's method to develop power series expansions of algebraic space curves is the use case for this application.