We consider solving a sparse linear system using integer (fixed-point) arithmetic. Integer arithmetic has attracted attention in scientific computing because of its high computational efficiency. Furthermore, considering the current circumstances of hardware development, integer arithmetic is expected to become increasingly important. Nevertheless, integer arithmetic has not been widely used for solving linear systems because it lacks robustness against overflow and underflow, making it hard to solve practical problems. Thus, we propose a new integer-based implementation framework for the flexible GMRES (FGMRES) method, which enables integer-based solvers to solve linear systems with the same accuracy as conventional floating-point solvers. In addition, we propose an integer-only algebraic multigrid preconditioner. Combining it with the integer-based FGMRES framework, we develop an integer-based solver. Numerical experiments on CPUs showed that the developed integer-based solver has a comparable convergence rate to floating-point solvers. We also found the test cases where the integer-based solver runs faster than the floating-point solvers.

Kengo Suzuki

Takeshi Fukaya

Takeshi Iwashita

ACM Transactions on Mathematical Software

作为一本科学期刊，ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE (TOMS) 记录了数值、符号、代数和几何计算应用的理论基础。它侧重于算法和程序的分析和构建，以及程序和架构的交互。 TOMS 中记录的算法可在 CALGO.ACM.ORG 上作为 ACM 的收集算法获得。

ACM Transactions on Mathematical Software (TOMS) is a scientific journal that focuses on the theoretical foundations of numerical, symbolic, algebraic, and geometric computation applications. It emphasizes the analysis and construction of algorithms and programs, as well as the interaction between programs and architectures. The algorithms recorded in TOMS are available as collected algorithms from ACM at CALGO.ACM.ORG.

《ACM Transactions on Mathematical Software》是一本科学期刊，专注于数值、符号、代数和几何计算应用的理论基础。期刊强调算法和程序的分析与构建，以及程序与架构之间的相互作用。TOMS中记录的算法可在CALGO.ACM.ORG上作为ACM的收集算法获得。

Category	Quartile
数学	1
数学, 计算机软件工程	1
数学, 应用数学	1

An integer arithmetic-based AMG preconditioned FGMRES solver

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Journal Info

Category	Quartile
MATHEMATICS, APPLIED	1