#### Topic: The effective decision big incompatible Slough

Kind time of days! There is certainly incompatible Slough (the order of 10000 variables and 40000 equations) for which it is necessary to search for the decision in sense of minimization of a discrepancy. System strongly rarefied - in each equation 1 or 2 variable, and remaining coefficients certainly zero. At a model development cycle in matlab for the decision of this task function mldivide which fulfilled less than for 0,1 was used. At a model rewriting on With ++ with Intel MKL usage the given code location began to be fulfilled ~10-50 seconds how I implemented it. If through direct usage QR of the solver (LAPACKE_dgels) on the dense matrix in the size 10*40 elements it turned out seconds 50 and a lot of storage on storage of all matrix (much more than consumed matlab). If through conversion to a type (A ^ {T} A) x = (A ^ {T} b) and search of the decision of this joint system (with the dense square matrix 10*10) with the help mkl_dcsrmv, mkl_dcsrmultd for conversion and LAPACKE_dgesv it is immediate for the decision I managed to receive time of the order of 10 seconds for the decision. It turns out that the difference in time with matlab - a minimum 2 orders that somehow is too much. Moreover, matlab in the virtual machine on 4-hletnem CPU, and Intel MKL on new server Xeon E5 v4 generally was launched. Prompt, please, that I can do not so? Can be eat the implemented methods of the fast decision of such strongly rarefied incompatible Sloughs about which I do not know and about which it is not told in the function description mldivide (where generally it is said, what for my case is used QR the solver)?