Semi-Analytical Solution of Brent Equations

A parametrization of Brent equations is proposed which leads to a several times reduction of the number of unknowns and equations. The arising equations are solved numerically using a nonlinear least squares method. Matrix multiplication algorithms that are faster than previously known ones are obtained. In particular, \((4,4,4;48)\) - and \((2,4,5;32)\) -algorithms are found.