论文标题
使用GMRES方法和迭代改进的基于整数的基于整数的稀疏线性求解器
An Integer Arithmetic-Based Sparse Linear Solver Using a GMRES Method and Iterative Refinement
论文作者
论文摘要
在本文中，我们基于整数算术开发了（预处理的）GMRES求解器，并为求解器引入一个迭代精致框架。我们描述了基于整数或固定点号的求解器的系数矩阵和向量的数据格式。为了避免计算的溢出，我们引入了算术操作中操作数的初始缩放和逻辑偏移（调整）。考虑到GMRES算法的特征，我们介绍了操作数转移的方法。数值测试表明，基于迭代精炼的整数基于整数的求解器具有相当的求解器性能，就基于浮点算术的收敛到标准求解器而言。此外，我们表明预处理很重要，不仅对于改善收敛性，而且还降低了溢出的风险。
In this paper, we develop a (preconditioned) GMRES solver based on integer arithmetic, and introduce an iterative refinement framework for the solver. We describe the data format for the coefficient matrix and vectors for the solver that is based on integer or fixed-point numbers. To avoid overflow in calculations, we introduce initial scaling and logical shifts (adjustments) of operands in arithmetic operations. We present the approach for operand shifts, considering the characteristics of the GMRES algorithm. Numerical tests demonstrate that the integer arithmetic-based solver with iterative refinement has comparable solver performance in terms of convergence to the standard solver based on floating-point arithmetic. Moreover, we show that preconditioning is important, not only for improving convergence but also reducing the risk of overflow.
