Interpolation | Articles containing proofs | Polynomials
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 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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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