Questions tagged [matrix-multiplication]

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Calculate boolean matrix multiplication (BMM) using transitive closure

Let us say I am given an algorithm that calculates the transitive closure of a given graph $G = \{ V, E \}$. How can I use this algorithm in order to perform the Boolean Matrix Multiplication of two ...
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Matrix-vector multiplication using only lower triangular of matrix

Suppose one has a large sparse symmetric positive definite matrix $A$ and wants to multiply it by a vector $x$. Only the lower triangular part of matrix A is stored/known. The multiplication $Ax$ ...
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Lower bounds for orthogonal matrix multiplication

Is it possible, according to the current state of knowledge, that orthogonal matrices can be multiplied faster than arbitrary matrices? More precisely, let $T(N)$ denote the worst-case time of the ...
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47 views

Merging the submatrices' time complexity in matrix multiplication

This is a problem of CLRS: What is the largest $k$ such that if you can multiply $3 \times 3$ matrices using $k$ multiplications (not assuming commutativity of multiplication), then you can multiply $...
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Best sparse matrix structure for Lanczos algorithm and/or matrix-vector multiplication

I have written a Lanczos routine which I am using for some problems in physics. Now, I would like to feed it some sparse matrices with very low densities (hamiltonians of large systems), and for that ...
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Why is the weight matrix diagonal in weighted least squares regression?

I was going through the theory for weighted least-squares fitting and I understood its basic underlying concepts, but I couldn't understand why exactly do we keep the weights as a diagonal matrix ...