Rayleigh quotient iteration is an eigenvalue algorithm which extends the idea of the inverse iteration by using the Rayleigh quotient to obtain increasingly accurate eigenvalue estimates. Rayleigh quotient iteration is an iterative method, that is, it delivers a sequence of approximate solutions that converges to a true solution in the limit. Very rapid convergence is guaranteed and no more than a few iterations are needed in practice to obtain a reasonable approximation. The Rayleigh quotient iteration algorithm converges cubically for Hermitian or symmetric matrices, given an initial vector that is sufficiently close to an eigenvector of the matrix that is being analyzed. (Wikipedia).
Power Method with Inverse & Rayleigh
Discussion of Eigenvalues & Eigenvectors, Power Method, Inverse Power Method, and the Rayleigh Quotient with brief overview of Rayleigh Quotient Iteration. Example code hosted on GitHub https://github.com/osveliz/numerical-veliz Chapters 0:00 Title Card 0:12 Terminology 0:37 Eigenvalue Ex
From playlist Numerical Methods
Rayleigh Quotient Based Numerical Methods for Eigenvalue Problems, Lecture 2
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From playlist Gene Golub SIAM Summer School Videos
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From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Lec 13 | MIT Finite Element Procedures for Solids and Structures, Nonlinear Analysis
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From playlist MIT Nonlinear Finite Element Analysis
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation
Today, we diagonialized some matrices, if you know what I mean... It was meant literally. That was what we did. -- Watch live at https://www.twitch.tv/simuleios
From playlist DMRG
Got the power method running, we can find 1 eigenvalue! -- Watch live at https://www.twitch.tv/simuleios
From playlist DMRG
Lec 12 | MIT Finite Element Procedures for Solids and Structures, Linear Analysis
Lecture 12: Solution methods for frequencies and mode shapes Instructor: Klaus-Jürgen Bathe View the complete course: http://ocw.mit.edu/RES2-002S10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Linear Finite Element Analysis
Illustrates the solution of a Bernoulli first-order differential equation. Free books: http://bookboon.com/en/differential-equations-with-youtube-examples-ebook http://www.math.ust.hk/~machas/differential-equations.pdf
From playlist Differential Equations with YouTube Examples
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From playlist Wolfram Technology Conference 2019
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From playlist Integrals
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From playlist Machine Learning
(ML 10.6) Predictive distribution for linear regression (part 3)
How to compute the (posterior) predictive distribution for a new point, under a Bayesian model for linear regression.
From playlist Machine Learning
SIAM's Gene Golub's Rayleigh Quotient Based Numerical Methods for Eigenvalue Problems, Lecture 1
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From playlist Gene Golub SIAM Summer School Videos
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From playlist Root Finding
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From playlist Gene Golub SIAM Summer School Videos
Use Picard's Iteration to Approximate a Solution to a IVP (2 iterations only)
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From playlist Linear First Order Differential Equations: Interval of Validity (Existence and Uniqueness)