In numerical mathematics, hierarchical matrices (H-matrices)are used as data-sparse approximations of non-sparse matrices. While a sparse matrix of dimension can be represented efficiently in units of storage by storing only its non-zero entries, a non-sparse matrix would require units of storage, and using this type of matrices for large problems would therefore be prohibitively expensive in terms of storage and computing time. Hierarchical matrices provide an approximation requiring only units of storage, where is a parameter controlling the accuracy of the approximation. In typical applications, e.g., when discretizing integral equations,preconditioning the resulting systems of linear equations,or solving elliptic partial differential equations, a rank proportional to with a small constant is sufficient to ensure an accuracy of . Compared to many other data-sparse representations of non-sparse matrices, hierarchical matrices offer a major advantage: the results of matrix arithmetic operations like matrix multiplication, factorization or inversion can be approximated in operations, where (Wikipedia).
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
Matrices: Leading Rows and leading Columns
What are leading rows and columns in a matrix? What are leading entries?
From playlist Intro to Linear Systems
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
Matrix Algebra Basics || Matrix Algebra for Beginners
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. This course is about basics of matrix algebra. Website: https://geekslesson.com/ 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add
From playlist Algebra
Jamie Haddock - Hierarchical and neural nonnegative tensor factorizations - IPAM at UCLA
Recorded 02 December 2022. Jamie Haddock of Harvey Mudd College presents "Hierarchical and neural nonnegative tensor factorizations" at IPAM's Multi-Modal Imaging with Deep Learning and Modeling Workshop. Abstract: Nonnegative matrix factorization (NMF) has found many applications includin
From playlist 2022 Multi-Modal Imaging with Deep Learning and Modeling
How to Cluster Data in MATLAB | K Means Clustering | Hierarchical Clustering in MATLAB | Simplilearn
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From playlist Matlab
Jamie Haddock: "Scaling the Hierarchical Topic Modeling Mountain: Neural NMF and Iterative Proje..."
Deep Learning and Medical Applications 2020 "Scaling the Hierarchical Topic Modeling Mountain: Neural NMF and Iterative Projection Methods" Jamie Haddock - University of California, Los Angeles (UCLA), Mathematics Abstract: Datasets with hierarchical structure arise in a wide variety of
From playlist Deep Learning and Medical Applications 2020
Hierarchical Interpolative Factorization
At the 2013 SIAM Annual Meeting, Lexing Ying of Stanford University discussed some recent results on developing new factorizations for matrices obtained from discretizing differential and integral operators. A common ingredient of these new factorizations is the interpolative decomposition
From playlist Complete lectures and talks: slides and audio
Data Science - Part VII - Cluster Analysis
For downloadable versions of these lectures, please go to the following link: http://www.slideshare.net/DerekKane/presentations https://github.com/DerekKane/YouTube-Tutorials This lecture provides an overview of clustering techniques, including K-Means, Hierarchical Clustering, and Gauss
From playlist Data Science
Unsupervised Learning | Unsupervised Learning Algorithms | Machine Learning Tutorial | Simplilearn
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Factorization-based Sparse Solvers and Preconditions, Lecture 5
Xiaoye Sherry Li's (from Lawrence Berkeley National Laboratory) lecture number five on Factorization-based sparse solves and preconditioners
From playlist Gene Golub SIAM Summer School Videos
Workshop on Theory of Deep Learning: Where next? Topic: Spotlight Talks Speakers: Yuanzhi Li, Soham De, Mahyar Fazlyab, Maithra Raghu, Valentin Thomas Date: October 15, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
6.4.6 R6. Segmenting Images - Video 4: MRI Image
MIT 15.071 The Analytics Edge, Spring 2017 View the complete course: https://ocw.mit.edu/15-071S17 Instructor: Nataly Youssef Segmenting a healthy MRI brain image using hierarchical clustering. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses
From playlist MIT 15.071 The Analytics Edge, Spring 2017
Linear Algebra 1.3 Matrices and Matrix Operations
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul
From playlist Linear Algebra
Singular Value Decomposition (SVD): Mathematical Overview
This video presents a mathematical overview of the singular value decomposition (SVD). These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz Amazon: https://www.amazon.com/Data-Driven-Science-En
From playlist Data-Driven Science and Engineering