The Aberth method, or Aberth–Ehrlich method or Ehrlich–Aberth method, named after Oliver Aberth and Louis W. Ehrlich, is a root-finding algorithm developed in 1967 for simultaneous approximation of all the roots of a univariate polynomial. This method converges cubically, an improvement over the Durand–Kerner method, another algorithm for approximating all roots at once, which converges quadratically. (However, both algorithms converge linearly at multiple zeros.) This method is used in MPSolve, which is the reference software for approximating all roots of a polynomial to an arbitrary precision. (Wikipedia).

The Aberth-Ehrlich Method for solving all roots of a polynomial simultaneously including history, methodology, examples, and order as well as comparison to Durand-Kerner. Example code github: http://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:19 History 0:41 Methodology 0:59

From playlist Root Finding

The Durand-Kerner Method for solving all roots of a polynomial simultaneously including complex solutions. Example code github: http://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:24 History 1:04 Methodology & Derivation 2:28 Example 1 real numbers 2:55 Example 2 need for comp

From playlist Root Finding

Laguerre's method for finding real and complex roots of polynomials. Includes history, derivation, examples, and discussion of the order of convergence as well as visualizations of convergence behavior. Example code available on github https://www.github.com/osveliz/numerical-veliz Chapte

From playlist Root Finding

Graeffe's Root-Squaring Method (also called Graeffe-Dandelin-Lobachevskiĭ or Dandelin–Lobachesky–Graeffe method) for finding roots of polynomials. The method solves for all of the roots of a polynomial by only using the coefficients and does not require derivatives nor an interation funct

From playlist Root Finding

Euler’s method - How to use it?

► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method,

From playlist Differential Equations

Horner's Method (Ruffini-Horner Scheme) for evaluating polynomials including a brief history, examples, Ruffini's Rule with derivatives, and root finding using Newton-Horner. Example code on GitHub https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:11 - History 1:33 - TLDR 1

From playlist Root Finding

Bairstow's Method for finding the roots of polynomials including complex roots. Discussion of method derivation, relation to synthetic division of two variables, stopping condition, selection of initial values, fractals, and historical context. Submission for Summer of Math Exposition 2 co

From playlist Root Finding

Medieval Europe: Crash Course European History #1

Our European history is going to start around 1500 with the Renaissance, but believe it or not, that is not the actual beginning of history in the continent. So, today, we're going to teach you the broad outlines of the so-called Middle Ages, and look at events like the Black Plague, the H

From playlist Back to School - Expanded

Quantum Integral. Gauss would be proud! I calculate the integral of x^2n e^-x^2 from -infinity to infinity, using Feynman's technique, as well as the Gaussian integral and differentiation. This integral appears over and over again in quantum mechanics and is useful for calculus and physics

From playlist Integrals

Gaussian Integral 7 Wallis Way

Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using a technique that is very similar to the

From playlist Gaussian Integral

How to Get Classical Physics from Quantum Mechanics

We tend to think of Classical Physics as straightforward and intuitive and Quantum Mechanics as difficult and conceptually challenging. However, this is not always the case! In classical mechanics, a standard technique for finding the evolution equations for a system is the method of least

From playlist Quantum Mechanics

Euler's method for estimating solution to non-separable first-order differential equations.

From playlist Advanced Calculus / Multivariable Calculus

Euler's method for solving non-separable differential equation by approximation.

From playlist Advanced Calculus / Multivariable Calculus

Fermi Inversion Factor Explained

https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video

From playlist Optoelectronic and Photonic Devices

Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (12 of 92) Time & Position Dependencies 1/3

Visit http://ilectureonline.com for more math and science lectures! In this video I will separate the time and position dependencies of the Schrodinger's equation, part 1/3. Next video in this series can be seen at: https://youtu.be/djlpmDUtIZY

From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION

Convolution Theorem: Fourier Transforms

Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.

From playlist Partial differential equations

RubyConf 2021 - Control methods like a pro: A guide to Ruby's awesomeness, ... by Masafumi Okura

Control methods like a pro: A guide to Ruby's awesomeness, a.k.a. metaprogramming by Masafumi Okura Do you know that methods are objects in Ruby? We can manipulate method objects just like other object, meaning that we can store them in variables, get information from them and wrap them i

From playlist RubyConf 2021

RubyConf 2015 - Messenger: The (Complete) Story of Method Lookup by Jay McGavren

Messenger: The (Complete) Story of Method Lookup by Jay McGavren You call a method on an object, and it invokes the instance method defined on the class. Simple. Except when the method isn't on the class itself, because it's inherited from a superclass. Or a singleton class, mixin, or ref

From playlist RubyConf 2015

https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. Wave impedanc

From playlist Electromagnetics

RubyConf 2015 - Ruby 2 Methodology by Akira Matsuda

Ruby 2 Methodology by Akira Matsuda This talk focuses on "Method" in Ruby. Although Method is the key feature of an OOP language like Ruby, Ruby's Method is still drastically evolving. This session is a quick tour on new features and changes around Method in recent versions of the Ruby l

From playlist RubyConf 2015