Matrix multiplication algorithms | Matrix theory | Numerical linear algebra
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 as counting the paths through a graph. Many different algorithms have been designed for multiplying matrices on different types of hardware, including parallel and distributed systems, where the computational work is spread over multiple processors (perhaps over a network). Directly applying the mathematical definition of matrix multiplication gives an algorithm that takes time on the order of n3 field operations to multiply two n × n matrices over that field (Θ(n3) in big O notation). Better asymptotic bounds on the time required to multiply matrices have been known since the Strassen's algorithm in the 1960s, but the optimal time (that is, the computational complexity of matrix multiplication) remains unknown. As of October 2022, the best announced bound on the asymptotic complexity of a matrix multiplication algorithm is O(n2.37188) time, given by Duan, Wu and Zhou announced in a preprint. This improves on the bound of O(n2.3728596) time, given by Josh Alman and Virginia Vassilevska Williams. However, this algorithm is a galactic algorithm because of the large constants and cannot be realized practically. (Wikipedia).
This video explains how to multiply matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Matrices
Matrix multiplication. How to multiply matrices. In this video I show you how we define the multiplication of matrices. As you will see, it is not so simply as multiplying two numbers. Matrices can only be multiplied when the number of columns in the first matrix is similar to the numb
From playlist Introducing linear algebra
► My Precalculus course: https://www.kristakingmath.com/precalculus-course In this video we’re talking about everything you need to know about matrix multiplication. We’ll start simple and look at what it means to multiply a matrix by a scalar, and then move on to multiplying matrices tog
From playlist Popular Questions
Matrix Addition, Subtraction, and Scalar Multiplication
This video shows how to add, subtract and perform scalar multiplication with matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
Ex 1: Matrix Multiplication (Basic)
This video provides examples of matrix multiplication. One example is defined and one example is undefined. Site: http://mathispower4u.com
From playlist Introduction to Matrices and Matrix Operations
Ex: Matrix Scalar Multiplication
This video explains how to perform scalar multiplication. Site: http://mathispower4u.com
From playlist Introduction to Matrices and Matrix Operations
This is the second video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with multiplying two matrices. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Matrices
Matej Balog - AlphaTensor: Discover faster matrix multiplication algorithms with RL - IPAM at UCLA
Recorded 27 February 2023. Matej Balog of DeepMind presents "AlphaTensor: Discovering faster matrix multiplication algorithms with RL" at IPAM's Artificial Intelligence and Discrete Optimization Workshop. Abstract: Improving the efficiency of algorithms for fundamental computational tasks
From playlist 2023 Artificial Intelligence and Discrete Optimization
This is a game changer! (AlphaTensor by DeepMind explained)
#alphatensor #deepmind #ai Matrix multiplication is the most used mathematical operation in all of science and engineering. Speeding this up has massive consequences. Thus, over the years, this operation has become more and more optimized. A fascinating discovery was made when it was sho
From playlist Papers Explained
On Matrix Multiplication and Polynomial Identity Testing - Robert Andrews
Computer Science/Discrete Mathematics Seminar I Topic: On Matrix Multiplication and Polynomial Identity Testing Speaker: Robert Andrews Affiliation: University of Illinois Urbana-Champaign Date: January 30, 2023 Determining the complexity of matrix multiplication is a fundamental problem
From playlist Mathematics
Expanders and Communication-Avoiding Algorithms - Oded Schwartz
Oded Schwartz Technical University Berlin January 25, 2010 Algorithms spend time on performing arithmetic computations, but often more on moving data, between the levels of a memory hierarchy and between parallel computing entities. Judging by the hardware evolution of the last few decades
From playlist Mathematics
The fastest matrix multiplication algorithm
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free, and hurry—the first 200 people get 20% off an annual premium subscription. 0:00 Multiplying Matrices the standard way 2:05 The Strassen Method for 2x2 Matrices 3:52 Large matrices via induction 7:25 The history
From playlist Cool Math Series
Joseph Landsberg: "Introduction to the Geometry of Tensors (Part 2/2)"
Watch part 1/2 here: https://youtu.be/v9lx4XN3w9c Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Introduction to the Geometry of Tensors (Part 2/2)" Joseph Landsberg - Texas A&M University - College Station, Mathematics Abstract: I will give a
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Introduction to Laplacian Linear Systems for Undirected Graphs - John Peebles
Computer Science/Discrete Mathematics Seminar II Topic: Introduction to Laplacian Linear Systems for Undirected Graphs Speaker: John Peebles Affiliation: Member, School of Mathematics Date: February 23, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
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From playlist Mathematics
14. Caching and Cache-Efficient Algorithms
MIT 6.172 Performance Engineering of Software Systems, Fall 2018 Instructor: Julian Shun View the complete course: https://ocw.mit.edu/6-172F18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63VIBQVWguXxZZi0566y7Wf Prof. Shun discusses associativity in caches, the idea
From playlist MIT 6.172 Performance Engineering of Software Systems, Fall 2018
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra