I consider 100 .100 real matrices A,B=Matrix(100,100,(i,j)->rand()) (with 12 significant digits). In general, ConditionNumber(A) is <10^5; also I choose Digits:=17.Theoretically, the complexity of the calculations of Determinant(A), CharacteristicPolynomial(A,x), A.B and MatrixInverse(A) are similar (~n^3). Yet, the times of these calculations are respectively: 0"13, 0"67, 0"60 and, what surprises me, 75" (moreover, I don't display any result).
My question: concerning the calculation of the inverse, where does this factor 100 come from ? Would Matlab be 100 times faster ? I do not see why this would be the case; in particular, the standard methods for the calculation of the inverse are easily programmable.
Thanks in advance.