Questions tagged [matrix-multiplication]
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17
questions
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Matrix Multiplication Verification
This question relates to the 2nd edition of Probability and Computation by Mitzenmacher and Upfal.
The authors then use the Law of Total Probability
My question concerns the line that begins with $\...
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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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1answer
54 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 $Ax$ ...
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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 ...
0
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1answer
44 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 ...
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1answer
102 views
Iterated multiplication of permutation matrices
Given $m$ matrices of size $n\times n$ each of which is promised to be a permutation is it in $\mathit{quasiAC}^0$ or $\mathit{AC}^0$ to multiply the permutations where
$m=\mathit{poly}(n)$
$m=\...
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1answer
42 views
matrix multiplication speedup when the matrix elements are 0, 1 and -1
I would like to compute matrix multiplication A * B where A is Nx3 and B is 3x3. We also ...
2
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1answer
228 views
In Strassen's algorithm, why does padding the matrices with zeros not affect the asymptopic complexity?
In Strassen's algorithm, why does padding the matrices with zeros, in order to multiply matrices that are not powers of 2, not affect the asymptopic complexity?
Hi, I was reading this question but I ...
5
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1answer
71 views
Is there a polynomial sized arithmetic formula for iterated matrix multiplication?
I found an article on Catalytic space which describes how additional memory (which must be returned to it's arbitrary, initial state) can be useful for computation. There's also an expository follow ...
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53 views
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 ...
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2answers
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What is the intuition behind Strassen's Algorithm?
I came across Strassen's algorithm for matrix multiplication, which has time complexity $O(n^{2.81})$, significantly better than the naive $O(n^3)$. Of course, there have been several other ...
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0answers
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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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1answer
83 views
Is this benchmark sufficient to consider my algorithm as an efficient matrix multiplication algorithm?
I built a matrix multiplication algorithm and now I need some thoughts about following benchmark.
C++ chrono:: high resolution clock Time(micro second)
(Dim)256--> (Naive algo ) 296807, (My algo) ...
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1answer
28 views
How can follow this this guide to construct a graph with matrix/reachability
Let's we have k matrices. For example we have 3 now, where first one is 8x5 ($a_1$ x $b_1$), second one is 5 x 6 ($a_2$ x $b_2$) and last one is 6 x 8 ($a_3$ x $b_3$). And our goal is to figure out ...
0
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1answer
64 views
In a LP problem Ax = b, how to solve for A instead of x?
I have a multi-objective linear programming problem of the form Ax = b, where A is a matrix and x and b are vectors. x is known, and I'm looking to minimise each row of b by solving for A.
Constraints ...
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1answer
50 views
Is matrix multiplication cheaper than inverse?
In wiki, it is shown that the time complexity of matrix multiplication and matrix inverse is similar. But people always to argue it is easier to do matrix multiplication rather than inverse. Is this ...
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1answer
227 views
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 ...
