Numerical analysis | Polynomials | Algebra
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. After the introduction of computers, this algorithm became fundamental for computing efficiently with polynomials. The algorithm is based on Horner's rule: This allows the evaluation of a polynomial of degree n with only multiplications and additions. This is optimal, since there are polynomials of degree n that cannot be evaluated with fewer arithmetic operations. Alternatively, Horner's method also refers to a method for approximating the roots of polynomials, described by Horner in 1819. It is a variant of the Newton–Raphson method made more efficient for hand calculation by the application of Horner's rule. It was widely used until computers came into general use around 1970. (Wikipedia).
Labeling a System by Solving Using Elimination Method
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
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
Solve a System of Equations Using Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Ch05n3: Roots of Polynomials; Horner’s Algorithm
Roots of Polynomials; Horner’s Algorithm Numerical Computation, chapter 5, additional video no 3. To be viewed after the regular videos of chapter 5, and additional video 2. Wen Shen, Penn State University, 2018.
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
Should we create a Dino-Chicken? – the Ethics of Making a Living-Biological Attraction
Could we bring back a dinosaur? and more importantly should we even do it? Today I will discuss the "Chickenosaurus" project of paleontologist Jack Horner and dive into the fascinating world of genetics and biology that exists in our not too distant future. I talk about everything from Jur
From playlist Paleontology Videos
Why don't they teach this simple visual solution? (Lill's method)
Today's video is about Lill's method, an unexpectedly simple and highly visual way of finding solutions of polynomial equations (using turtles and lasers). After introducing the method I focus on a couple of stunning applications: pretty ways to solve quadratic equations with ruler and com
From playlist Recent videos
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
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
C46 Solving the previous problem by another method
There are more ways than one to solve Cauchy-Euler equations. In this video I revert to the substitution method.
From playlist Differential Equations
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
Using a Multiplier to Solve the System of Equations Using Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
The Fast Fourier Transform Without the Fourier?
An introduction to the Fast Fourier Transform from the perspective of multiplying polynomials. Great video on the geometric intuition behind the Fourier transform: https://www.youtube.com/watch?v=spUNpyF58BY&vl=en Article on big-O notation (one of the authors might be familiar...): ht
From playlist Summer of Math Exposition Youtube Videos
Solve a System of Linear Equations Using Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
C34 Expanding this method to higher order linear differential equations
I this video I expand the method of the variation of parameters to higher-order (higher than two), linear ODE's.
From playlist Differential Equations
Wittig & HWE Reactions - Alkene Synthesis (IOC 39)
I apologize that I pronounced 'Wittig' incorrectly in the introduction. In this episode, I discuss the Wittig & Horner-Wadsworth-Emmons reactions. These reactions are useful for the synthesis of alkenes. -----------------------------------------------------------------------------------
From playlist Organic Chemistry Lectures
Using two multipliers when solving a system of equations using the addition method
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Solve a System of Linear Equations Using Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
Solve a System of Linear Equations Using Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
Solve a System of Linear Equations Using Elimination
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
CSUN Chemistry and Biochemistry department 2nd Semester Organic Chemistry Lab How to do a Recrystallization: https://youtu.be/msUR4Q32vcI Horner Emmons Day 1: https://youtu.be/Ohoh_OyLE3s Made by Benjamin D. Azmon
From playlist Lab Technique