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Topic: Reversal of product of matrixes

All greetings, Are matrix A of dimensionality MxN where M the order 1000-3000, and N it is much more - hundred thousand, millions. It is required to find reverse for matrix B = A T*A dimensionalities MxM. 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?

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Re: Reversal of product of matrixes

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? Singular expansion A=USV* Then B = V* T S 2 V. Here V and S - small (dimensionality). To invert B in such representation it is simple. Like there are iterative algorithms for truncated SVD, type of Lantsosha or iterations of Arnoldi. Can will faster than multiply A T*A

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Re: Reversal of product of matrixes

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 .

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Re: Reversal of product of matrixes

Hello, kfmn, you wrote: K> There is 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. And it is really necessary to calculate a reciprocal matrix or it is necessary to find the normal decision of any system . The equations?

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Re: Reversal of product of matrixes

K> There is 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. Conjugate Gradient?