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Matrix multiplication algorithm

Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms efficient. Applications of matrix multiplication in computational problems are found in many fields including scientific computing and pattern recognition and in seemingly unrelated problems such…

Science, Sub-cubic algorithms & Parallel and distributed algorithms

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Sub-cubic algorithms

Volker Strassen Subtraction Numerical stability BLAS Finite fields

16 related topics

Parallel and distributed algorithms

Divide-and-conquer algorithm Parallelized Shared-memory multiprocessors Fork–join style Pseudocode

12 related topics

Overview

Matrix multiplication Numerical algorithms Scientific computing Pattern recognition Graph

16 related topics

Iterative algorithm

Simple algorithm Asymptotic notation Memory access patterns Fully associative cache Row-major order, column-major order

6 related topics

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Overview

Matrix multiplication
Numerical algorithms Numerical algorithm
Scientific computing
Pattern recognition
Graph Graph (graph theory)
Parallel Parallel computing
Distributed Distributed computing
Takes time Analysis of algorithms
Field Field (mathematics)
Big O notation
Asymptotic bounds Asymptotic bound
Strassen's algorithm Strassen algorithm
Computational complexity of matrix multiplication
Asymptotic complexity Time complexity
Williams Virginia Vassilevska Williams
Galactic algorithm

Iterative algorithm

Simple algorithm
Asymptotic notation
Memory access patterns Locality of reference
Fully associative cache CPU cache
Row-major order, column-major order Row- and column-major order
Tiled Loop tiling

Cache behavior

Cache-oblivious Cache-oblivious algorithm
Multiprogramming

Divide-and-conquer algorithm

Divide-and-conquer algorithm
Block partitioning Block matrix
Recursively Recursion
Scalar multiplication
Master theorem for divide-and-conquer recurrences Master theorem (analysis of algorithms)
Unrolled Loop unrolling

Sub-cubic algorithms

Volker Strassen
Subtraction
Numerical stability
BLAS Basic Linear Algebra Subprograms
Finite fields Finite field
Computer algebra systems Computer algebra system
Theoretical computer science
Real number
Don Coppersmith
Shmuel Winograd
Victor Pan
Freivalds' algorithm
Monte Carlo algorithm
DeepMind
Neural network
Finite field Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } GF(2)

Parallel and distributed algorithms

Divide-and-conquer algorithm Matrix multiplication algorithm
Parallelized Parallel algorithm
Shared-memory multiprocessors Shared-memory multiprocessor
Fork–join style Fork–join model
Pseudocode
Critical path length
Speedup
Distributed memory
Cannon's algorithm
Communication-avoiding algorithm
MapReduce
Meshes Mesh networking

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Matrix multiplication algorithm

Nodes65

Edges64

Triples22

Avg. degree1.97

Density0.030769

Components1

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Matrix multiplication algorithm

Top relations

related to AlphaTensor · 14

Matrix multiplication algorithm → AlphaTensor, Based, DeepMind, Deepmind's, Finding, In, NP-hard, On, Operations, Similarly, Some, Strassen's, Strassen’s, The

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Important terminology

algorithm matrix matrices multiplication fork algorithms multiply time cache two c11 case n3 parallel size partition t11 add iterative using

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
counting the paths through a graph	instance of	Applications of matrix multiplication in computational problems are found in many fields including scientific computing and pattern recognition and in seemingly unrelated problems	0.80	text
finite fields	instance of	It is very useful for large matrices over exact domains	0.80	text
where numerical stability is not an issue.Since Strassen's algorithm is actually used in practical numerical software	instance of	It is very useful for large matrices over exact domains	0.80	text
computer algebra systems	instance of	It is very useful for large matrices over exact domains	0.80	text
improving on the constants hidden in the big-O notation has its merits	instance of	It is very useful for large matrices over exact domains	0.80	text
MapReduce	instance of	On modern distributed computing environments	0.80	text
specialized multiplication algorithms have been developed.Algorithms for meshesThere are a variety of algorithms for multiplication on meshes	instance of	On modern distributed computing environments	0.80	text
specialized multiplication algorithms have been developed	instance of	On modern distributed computing environments	0.80	text
Matrix multiplication algorithm	related to AlphaTensor	In	0.60	section
Matrix multiplication algorithm	related to AlphaTensor	DeepMind	0.60	section
Matrix multiplication algorithm	related to AlphaTensor	AlphaTensor	0.60	section
Matrix multiplication algorithm	related to AlphaTensor	Operations	0.60	section

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