Abstract
Novel fast algorithms for multiplying square complex matrices are presented. The algorithms are based on concepts from fast methods of complex multiplication in which a surrogate is used for the square root of minus one. Previous methods imposed the structure of a finite ring or field on the problem. The novel algorithms also use a surrogate, but do not require the imposed structure and its inherent rounding. The number of real matrix multiplications required can be reduced from four to two for even dimension, and to 2+1/N/sup 2/ for odd dimension N. The disadvantage of the algorithms is the imposition of a requirement on the structure of one of the two complex matrices being multiplied. The 2*2 case of the algorithm can be adapted to computing Givens rotations, resulting in a 17% savings in real matrix multiplications. >
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