Hello, Mazay, you wrote: M> Hello, kfmn, you wrote: K>> All greetings, K>> Are matrix A of dimensionality MxN where M the order 1000-3000, and N it is much more - hundred thousand, millions. K>> It is required to find reverse for matrix B = A T*A dimensionalities MxM. K>> If to go a standard way calculation of this matrix slow enough, reversal - too not fast. Whether there is any algorithmic trick which would allow to accelerate process at the expense of that knowledge, what from itself represents B? M> Singular expansion A=USV* M> Then B = V* T S V. M> Here V and S - small (dimensionality). To invert B in such representation it is simple. M> like there are iterative algorithms for truncated SVD, type of Lantsosha or iterations of Arnoldi. Can will faster than multiply A T*A Yes, thought about it, but for some reason decided that it will be considered not faster, than reversal. . The Matrix V huge, same as A, on multiplication precisely I will benefit nothing, about reversal here I do not know. I will try, thanks, and suddenly .