分裂八元数乘法的一种算法
An algorithm for multiplication of split-octonions
摘要：
本文介绍了分裂八元数乘法的有效算法。两个分裂八元数的直接乘法需要64次实数乘法和56次实数加法。更有效的解决方案仍然不存在。我们展示了如何计算分裂八元数与28个实乘法和92个实加法的乘积。在所讨论的算法的合成过程中，我们使用了两个分裂八元数的乘积可以表示为向量矩阵乘积的事实。参与乘积计算的矩阵具有独特的结构属性，允许执行其有利的分解。也就是说，这种分解导致分裂八元数乘法的乘法复杂性显着降低。
英文摘要：
In this paper we introduce efficient algorithm for the multiplication of split-octonions. The direct multiplication of two split-octonions requires 64 real multiplications and 56 real additions. More effective solutions still do not exist. We show how to compute a product of the split-octonions with 28 real multiplications and 92 real additions. During synthesis of the discussed algorithm we use the fact that product of two split-octonions may be represented as vector-matrix product. The matrix that participates in the product calculating has unique structural properties that allow performing its advantageous decomposition. Namely this decomposition leads to significant reducing of the multiplicative complexity of split-octonions multiplication.
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