arXiv subjects

Kengo Suzuki

Publications and source records attributed to Kengo Suzuki.

3 recordsLinked to original sources

arXiv2026

PackSELL: A Sparse Matrix Format for Precision-Agnostic High-Performance SpMV

We propose a new sparse matrix format, PackSELL, designed to support diverse data representations and enable efficient sparse matrix-vector multiplication (SpMV) on GPUs. Building on sliced ELLPACK (SELL), PackSELL incorporates delta encoding of column indices and a novel packing scheme that stores each index-delta-value pair in a single word, thereby reducing memory footprint and data movement. This design further enables fine-grained control over the bit allocation between deltas and values, allowing flexible data representations, including non-IEEE formats. Experimental results show that, when configured for half precision (FP16), the PackSELL-based SpMV kernel outperforms the cuSPARSE SELL-based kernel by up to $1.63\times$. Moreover, with configurations using customized formats, PackSELL achieves FP32-level accuracy while exceeding the performance of FP16 cuSPARSE. These benefits extend to sparse linear solvers; for example, a mixed-precision preconditioned conjugate gradient (PCG) solver using PackSELL achieves up to a $2.09\times$ speedup over the standard full-precision PCG.

cs.DC↗

arXiv2025

A Nested Krylov Method Using Half-Precision Arithmetic

Low-precision computing is essential for efficiently utilizing memory bandwidth and computing cores. While many mixed-precision algorithms have been developed for iterative sparse linear solvers, effectively leveraging half-precision (fp16) arithmetic remains challenging. This study introduces a novel nested Krylov approach that integrates the flexible GMRES and Richardson methods in a deeply nested structure, progressively reducing precision from double-precision to fp16 toward the innermost solver. To avoid meaningless computations beyond precision limits, the low-precision inner solvers perform only a few iterations per invocation, while the nested structure ensures their frequent execution. Numerical experiments show that using fp16 in the approach directly enhances solver performance without compromising convergence, achieving speedups of up to 1.65x and 2.42x over double-precision and double-single mixed-precision implementations, respectively. Moreover, the proposed method outperforms or matches other standard Krylov solvers, including restarted GMRES, CG, and BiCGStab methods.

math.NA↗

arXiv2021

An Integer Arithmetic-Based Sparse Linear Solver Using a GMRES Method and Iterative Refinement

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.

math.NA↗