In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization of tensor hardware supporting low precision has gained increasing prominence in scientific research. However, the use of low-precision tensor hardware for computational acceleration often introduces errors, posing a fundamental challenge of simultaneously achieving effective acceleration while maintaining computational accuracy. This paper proposes improvements in the methodology by incorporating low-precision quantization and employing a residual matrix for error correction and combines vector-wise quantization method.. The key innovation lies in the use of sparse matrices instead of dense matrices when compensating for errors with a residual matrix. By focusing solely on values that may significantly impact relative errors under a specified threshold, this approach aims to control quantization errors while reducing computational complexity. Experimental results demonstrate that this method can effectively control the quantization error while maintaining high acceleration effect.The improved algorithm on the CPU can achieve up to 15\% accuracy improvement while 1.46 times speed improvement.

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