论文标题
矩阵快速乘法乘以其转置
On fast multiplication of a matrix by its transpose
论文作者
论文摘要
We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field.We use geometric considerations on the space of bilinear forms describing 2x2 matrix products to obtain this algorithm and we show how to reduce the number of involved additions.The resulting algorithm for arbitrary dimensions is a将矩阵通过其转置向一般矩阵产物的乘法减少，从而通过先前已知的恒定因子进行改进。在本文中，我们提出的时间表具有低内存足迹的时间表，以支持在有限领域的快速和记忆有效实施实现。总结说，我们在LDLT分支中显示如何在LDLT分支中使用结果。
We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field.We use geometric considerations on the space of bilinear forms describing 2x2 matrix products to obtain this algorithm and we show how to reduce the number of involved additions.The resulting algorithm for arbitrary dimensions is a reduction of multiplication of a matrix by its transpose to general matrix product, improving by a constant factor previously known reductions.Finally we propose schedules with low memory footprint that support a fast and memory efficient practical implementation over a finite field.To conclude, we show how to use our result in LDLT factorization.
