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# Questions tagged [matrix-multiplication]

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### runtime of solving matrix differential equation wrt dimensions of matrix

Suppose a computer solves a coupled differential equations (with given boundary conditions) of which each equation deals with $2^n \times 2^n$ size of matrices as solutions. My question is Does time-...
37 views

### fast multiplication of power of a matrix by a vector

I'm interested in computing of the product $M^n v$, where $M$ is an $m\times m$ matrix (over a semiring) and $v$ is column-vector, with the smallest number of multiplications in the underlying ...
79 views

### Best-known complexity for $l \times m$ by $m \times n$ matrix multiplication?

I know that the fastest known algorithm for multiplying two $m \times m$ matrices runs in time $m^{\omega}$, where currently we have $\omega = 2.3728596$ due to Virginia Williams's latest result (see ...
• 5,144
47 views

### Computing a series of matrix power - matrix products

Assuming we have two dense matrices $A \in \mathbb{R}^{m\times m}, B \in \mathbb{R}^{m\times n}$, is there a smart way to compute all entries of the series $A^1 B, A^2 B, A^3 B, \dots, A^k B$ up to ...
• 31
1 vote
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• 377
1 vote
111 views

### 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 $Ax$ ...
• 11
17 views

### 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 ...
• 101
61 views

### Why do researchers only count the number of multiplications when analyse the time complexity of Matrix Multiplication?

In this article about the recent breakthough in Matrix Multiplication, it quotes Chris Umans's words: Multiplications are everything. The exponent on the eventual running time is fully dependent only ...
• 570
1 vote