On the inequivalence of bilinear algorithms for 3×33×3 matrix multiplication

Since Laderman showed an algorithm for 3x3 matrix multiplication using 23 scalar multiplications, Johnson and McLoughlin used a numerical optimization and human controlled method to give two parameterized algorithms in which the coefficients are rational numbers. The algorithms are inequivalent to [email protected]?s one with respect to the transformation introduced by de Groote. We present a simple and fast numerical heuristic for finding valid algorithms. Then we show that many of the obtained algorithms are inequivalent to the published ones.