Abstract: Focusing on the trade-off in terms of speed, accuracy and efficiency between the exact and approximate algorithms for large-scale matrix multiplication, this paper proposed a fast algorithm for dense matrix multiplication employing regularization, filtering, and resampling techniques. Based on the sampling theorem, a regularization relationship between the matrix and its corresponding analog function was established, and then filtering and resampling stages were introduced to achieve the trade-off mechanism between the exact algorithm and the approximate algorithm. In pursuit of higher algorithmic efficiency, the applicable scope and conditions of the algorithm were investigated, especially the relationship between the algorithm accuracy and the statistical characteristics of the matrix data. Data experiments were conducted using matrices generated by methods such as independent and identically distributed random number generators. The results indicate that the algorithm achieves its trade-off objectives.

Key words: matrix multiplication, fast algorithm, sampling theorem, regularization