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Lagrange polynomial

In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data set of coordinate pairs with the are called nodes and the are called values. The Lagrange polynomial has degree and assumes each value at the corresponding node, Although named after Joseph-Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring. It is also an easy consequence of a formula published in 1783 by Leonhard Euler. Uses of Lagrange polynomials include the Newton–Cotes method of numerical integration and Shamir's secret sharing scheme in cryptography. For equispaced nodes, Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation. (Wikipedia).

Lagrange polynomial
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Lagrange Polynomials

Lagrange Polynomials for function approximation including simple examples. Chapters 0:00 Intro 0:08 Lagrange Polynomials 0:51 Visualizing L2 1:00 Numeric Example 1:11 Example Visualized 1:27 Why Lagrange Works 1:47 Lagrange Accuracy 2:12 Error 2:59 Error Visualized 3:20 Error Bounds 4:08

From playlist Numerical Methods

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Untold connection: Lagrange and ancient Chinese problem

Lagrange interpolating polynomial and an ancient Chinese problem is actually connected! It is a surprising connection, and a very inspiring one at the same time. It tells us that Mathematics has much more to discover! Lagrange interpolating polynomial is normally see as a statistical meth

From playlist Modular arithmetic

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Calculus BC - Unit 5 Lesson 2: Lagrange Error Bound

Calculus BC - Taylor's Remainder Theorem and the Lagrange Error Bound

From playlist AP Calculus BC

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Number Theory | Lagrange's Theorem of Polynomials

We prove Lagrange's Theorem of Polynomials which is related to the number of solutions to polynomial congruences modulo a prime.

From playlist Number Theory

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Lagrange Multipliers Maximum of f(x, y, z) = xyz subject to x + y + z - 3 = 0

Lagrange Multipliers Maximum of f(x, y, z) = xyz subject to x + y + z - 3 = 0

From playlist Calculus 3

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Ch02n1: Barycentric forms of Lagrange polynomials

Barycentric forms of Lagrange polynomials. Numerical Computation, Chapter 2, additional video no 1. To be viewed after video ch2.2. Wen Shen, Penn State, 2018.

From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University

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Math 031 Spring 2018 043018 Lagrange Remainder Theorem

Definition of Taylor polynomial; of remainder (error). Statement of Lagrange Remainder Theorem. Example.

From playlist Course 3: Calculus II (Spring 2018)

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Lagrange theorem

We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at

From playlist Abstract algebra

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Maximize a Function of Two Variable Under a Constraint Using Lagrange Multipliers

This video explains how to use Lagrange Multipliers to maximize a function under a given constraint. The results are shown in 3D.

From playlist Lagrange Multipliers

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Lagrange Interpolation

A basic introduction to Lagrange Interpolation. Chapters 0:00 Introduction 01:07 Lagrange Polynomials 03:58 The Lagrange Interpolation formula 05:10 The Resulting Polynomials The product links below are Amazon affiliate links. If you buy certain products on Amazon soon after clicking th

From playlist Interpolation

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What are Reed-Solomon Codes?

An introduction to Modular Arithmetic, Lagrange Interpolation and Reed-Solomon Codes. Sign up for Brilliant! https://brilliant.org/vcubingx Fund future videos on Patreon! https://patreon.com/vcubingx The source code for the animations can be found here: https://github.com/vivek3141/videos

From playlist Other Math Videos

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More bases of polynomial spaces | Wild Linear Algebra A 21 | NJ Wildberger

Polynomial spaces are excellent examples of linear spaces. For example, the space of polynomials of degree three or less forms a linear or vector space which we call P^3. In this lecture we look at some more interesting bases of this space: the Lagrange, Chebyshev, Bernstein and Spread po

From playlist WildLinAlg: A geometric course in Linear Algebra

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ch2 2: polynomial interpolation, Lagrange form. Wen Shen

Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I

From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University

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Mod-01 Lec-03 Interpolating Polynomials

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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Worked example: estimating sin(0.4) using Lagrange error bound | AP Calculus BC | Khan Academy

Lagrange error bound (also called Taylor remainder theorem) can help us determine the degree of Taylor/Maclaurin polynomial to use to approximate a function to a given error bound. See how it's done when approximating the sine function. Watch the next lesson: https://www.khanacademy.org/m

From playlist Series | AP Calculus BC | Khan Academy

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Secret Sharing Schemes

Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist Computer - Cryptography and Network Security

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Linear Algebra 12c: Applications Series - Polynomial Interpolation According to Lagrange

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

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Taylor Polynomials & Estimation Error, Lagrange Remainder Calculus 2 BC

I work through 5 examples of finding nth Taylor Polynomial and Maclaurin Polynomials to estimate the value of any function. I also find the maximum possible error, the Lagrange remainder form, for a given estimation. Note: Z came from weighted mean value theorem when applied to the inte

From playlist Calculus 2

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Hermite interpolation | Numerical integration | Indeterminate form | Chinese remainder theorem | Runge's phenomenon | Table of Newtonian series | Finite field | Linear algebra | Newton–Cotes formulas | Carlson's theorem | Kronecker delta | Identity matrix | Polynomial interpolation | Polynomial | Sylvester's formula | Bernstein polynomial | Newton polynomial | Vandermonde matrix | Degree of a polynomial | Cryptography | Chebyshev nodes | Edward Waring | Divided differences | Finite difference coefficient | Fast Fourier transform | Chebfun | Numerical analysis | Graph of a function | Joseph-Louis Lagrange | Rolle's theorem | Shamir's Secret Sharing | Frobenius covariant | Leonhard Euler | Neville's algorithm | Monomial basis