一种低乘法复杂度的双曲八元数乘法算法的推导
Derivation of a low multiplicative complexity algorithm for multiplying hyperbolic octonions
摘要：
提出了一种双曲八元数相乘的有效算法。两个双曲八元数的直接乘法需要64次实乘法和56次实加法。更有效的解决方案仍然不存在。我们展示了如何计算一个产品的双曲八元数与26个真正的乘法和92个真正的加法。在所讨论的算法的合成过程中，我们使用了两个双曲八元数的乘积可以表示为矩阵向量乘积的事实。参与乘积计算的矩阵被乘数具有独特的结构性质，允许执行其有利的因式分解。即这种因式分解导致双曲八元数乘法的计算复杂性的显著降低。
英文摘要：
We present an efficient algorithm to multiply two hyperbolic octonions. The direct multiplication of two hyperbolic 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 hyperbolic octonions with 26 real multiplications and 92 real additions. During synthesis of the discussed algorithm we use the fact that product of two hyperbolic octonions may be represented as a matrix - vector product. The matrix multiplicand that participates in the product calculating has unique structural properties that allow performing its advantageous factorization. Namely this factorization leads to significant reducing of the computational complexity of hyperbolic octonions multiplication.
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