Divide-and-conquer algorithms | Numerical linear algebra
Divide-and-conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have recently (circa 1990s) become competitive in terms of stability and efficiency with more traditional algorithms such as the QR algorithm. The basic concept behind these algorithms is the divide-and-conquer approach from computer science. An eigenvalue problem is divided into two problems of roughly half the size, each of these are solved recursively, and the eigenvalues of the original problem are computed from the results of these smaller problems. Here we present the simplest version of a divide-and-conquer algorithm, similar to the one originally proposed by Cuppen in 1981. Many details that lie outside the scope of this article will be omitted; however, without considering these details, the algorithm is not fully stable. (Wikipedia).
Google and eigenvalues. We describe the Pagerank algorithm, which was one of the algorithms used by Google for their search engine. For this, we rank the websites using an importance vector vector and write the system as a Markov chain, using matrices. Then we diagonalize the matrix using
From playlist Eigenvalues
Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (23 of 35) The Power Method with Scaling
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the dominant eigenvector and the corresponding eigenvalue using the power method with scaling (2x2 matrix). Next video in this series can be seen at: https://youtu.be/6StS7VjtuGI
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS
The method of determining eigenvalues as part of calculating the sets of solutions to a linear system of ordinary first-order differential equations.
From playlist A Second Course in Differential Equations
Eigenvalue Power Method (Example) | Lecture 31 | Numerical Methods for Engineers
Illustration of the power method for computing the dominant eigenvalue and eigenvector of a matrix. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel
From playlist Numerical Methods for Engineers
matrix choose a matrix. Calculating the number of matrix combinations of a matrix, using techniques from linear algebra like diagonalization, eigenvalues, eigenvectors. Special appearance by simultaneous diagonalizability and commuting matrices. In the end, I mention the general case using
From playlist Eigenvalues
Eigenvalue Power Method | Lecture 30 | Numerical Methods for Engineers
How to compute the dominant eigenvalue using the power method. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasno
From playlist Numerical Methods for Engineers
Anders Nikklasson - Quantum-Mechanical Molecular Dynamics for Distributed Computing and AI-hardware
Recorded 27 March 2023. Anders Nikklasson of Los Alamos National Laboratory presents "Quantum-Mechanical Molecular Dynamics for Distributed Computing and AI-hardware" at IPAM's Increasing the Length, Time, and Accuracy of Materials Modeling Using Exascale Computing workshop. Abstract: We p
From playlist 2023 Increasing the Length, Time, and Accuracy of Materials Modeling Using Exascale Computing
(3.4.103) Solve a Linear System of ODEs using the Eigenvalue Method: Real, Distinct Eigenvalues
This video explains how to solve a linear first order system of ODEs using the Eigenvalue method with 2 real, distinct eigenvalues. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Lec 13 | MIT 18.085 Computational Science and Engineering I
Numerical linear algebra: orthogonalization and A = QR A more recent version of this course is available at: http://ocw.mit.edu/18-085f08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2007
8ECM Invited Lecture: Daniel Kressner
From playlist 8ECM Invited Lectures
Reducing Isotropy to KLS: An Almost Cubic Volume Algorithm by Santosh Vempala
Program Advances in Applied Probability II (ONLINE) ORGANIZERS: Vivek S Borkar (IIT Bombay, India), Sandeep Juneja (TIFR Mumbai, India), Kavita Ramanan (Brown University, Rhode Island), Devavrat Shah (MIT, US) and Piyush Srivastava (TIFR Mumbai, India) DATE: 04 January 2021 to 08 Januar
From playlist Advances in Applied Probability II (Online)
Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (21 of 35) Find the Dominant Eigenvectors=?
Visit http://ilectureonline.com for more math and science lectures! In this video I will find eigenvector(s)=? using the approximation method where A is a 2x2 matrix. Next video in this series can be seen at: https://youtu.be/DLg9qDoL8Hs
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS
Universality aspects in numerical computation - Percy Deift
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From playlist Mathematics
Lecture 7. Graph partitioning algorithms.
Network Science 2021 @ HSE http://www.leonidzhukov.net/hse/2021/networks/
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Network Science. Lecture11.Graph partitioning algorithms
Graph partitioning algorithms Lecture slides: http://www.leonidzhukov.net/hse/2020/networks/lectures/lecture11.pdf
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Universality in numerical computations with random data. Case studies - Percy Deift
Analysis Math-Physics Seminar Topic: Universality in numerical computations with random data. Case studies Speaker: Percy Deift Affiliation: New York University Date: Oct 13, 2016 For more videos, visit http://video.ias.edu
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Structured Regularization Summer School - L. Rosasco - 4/4 - 22/06/2017
Lorenzo Rosasco (Genova and MIT): Regularization Methods for Large Scale Machine Learning Abstract: Regularization techniques originally developed to solve linear inverse problems can be extended to derive nonparametric machine learning methods. These methods perform well in practice and
From playlist Structured Regularization Summer School - 19-22/06/2017
(3.4.104) Solve a Linear System of ODEs using the Eigenvalue Method: Imaginary Eigenvalues
This video explains how to solve a linear first order system of ODEs using the Eigenvalue method with 2 imaginary eigenvalues. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Joseph Bengeloun - Quantum Mechanics of Bipartite Ribbon Graphs...
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