Parallel Verified Linear System Solver for Uncertain Input Data

• Mariana Kolberg PUCRS
• Márcio Dorn PUCRS
• Luiz Gustavo Fernandes PUCRS
• Gerd Bohlender Universitaet Karlsruhe

Resumo

This paper presents a new parallel implementation for solving dense interval linear systems with verified computing. The use of intervals appears as one possible way to handle the uncertainty of input data in real problems. A verified method using midpoint-radius arithmetic and directed roundings was combined with optimized libraries such as SCALAPACK and PBLAS to provide a free, fast, reliable and accurate solver. Accuracy and performance results for executing this implementation in a cluster are shown. It is the authors opinion that the combination of verified and parallel computing is a powerful tool that could be used for several other mathematical problems.

Palavras-chave: Linear systems, Libraries, High performance computing, Equations, Arithmetic, Vectors, Linear algebra, Concurrent computing, Uncertainty, Optimization methods, Parallel Computing, Verified Computing, Linear Systems, Interval Arithmetic, Uncertain Input Data