Complexity classes | Approximation algorithms

Polynomial-time approximation scheme

In computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems). A PTAS is an algorithm which takes an instance of an optimization problem and a parameter ε > 0 and produces a solution that is within a factor 1 + ε of being optimal (or 1 – ε for maximization problems). For example, for the Euclidean traveling salesman problem, a PTAS would produce a tour with length at most (1 + ε)L, with L being the length of the shortest tour. The running time of a PTAS is required to be polynomial in the problem size for every fixed ε, but can be different for different ε. Thus an algorithm running in time O(n1/ε) or even O(nexp(1/ε)) counts as a PTAS. (Wikipedia).

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Polynomial approximation of functions (part 1)

Using a polynomial to approximate a function at f(0). More free lessons at: http://www.khanacademy.org/video?v=sy132cgqaiU

From playlist Calculus

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Polynomial approximations -- Calculus II

This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.

From playlist Calculus II

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Using Taylor Polynomials to Approximate Functions

This video shows how to determine a Taylor Polynomial to approximate a function. http://mathispower4u.yolasite.com/

From playlist Infinite Sequences and Series

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Linear Approximations and Differentials

Linear Approximation In this video, I explain the concept of a linear approximation, which is just a way of approximating a function of several variables by its tangent planes, and I illustrate this by approximating complicated numbers f without using a calculator. Enjoy! Subscribe to my

From playlist Partial Derivatives

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Polynomial approximation of functions (part 2)

Approximating a function with a polynomial by making the derivatives equal at f(0) (Maclauren Series) More free lessons at: http://www.khanacademy.org/video?v=3JG3qn7-Sac

From playlist Calculus

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Convolutions and Polynomial Approximation

In this video, I intuitively explain and apply some deeper mathematical tools - namely convolutions and approximate identities - to prove the Weierstrass approximation theorem, which roughly states that any continuous function can be approximated by polynomials. I also make connections to

From playlist Summer of Math Exposition Youtube Videos

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Taylor polynomials + functions of two variables

Download the free PDF http://tinyurl.com/EngMathYT This is a basic tutorial on how to calculate a Taylor polynomial for a function of two variables. The ideas are applied to approximate a difficult square root. Such concepts are seen in university mathematics.

From playlist Several Variable Calculus / Vector Calculus

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Error bounds for Taylor approximations -- Calculus II

This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.

From playlist Calculus II

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Richard Lassaigne: Introduction à la théorie de la complexité

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Mathematical Aspects of Computer Science

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Frédéric Vivien : Algorithmes d’approximation - Partie 2

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From playlist Mathematical Aspects of Computer Science

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Mod-01 Lec-01 Introduction and Overview

Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org

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Adeline Roux-Langlois : Using structured variants in lattice-based cryptography - Lecture 2

CONFERENCE Recording during the thematic meeting : « Francophone Computer Algebra Days» the March 07, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIR

From playlist Mathematical Aspects of Computer Science

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Chaitanya Swamy: Signaling in Bayesian Games

We study the optimization problem faced by an informed principal in a Bayesian game, who can reveal some information about the underlying random state of nature to the players (thereby influencing their payoffs) so as to obtain a desirable equilibrium. This yields the following signaling p

From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"

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Maria Charina: Algebraic multigrid and subdivision

Abstract: Multigrid is an iterative method for solving large linear systems of equations whose Toeplitz system matrix is positive definite. One of the crucial steps of any Multigrid method is based on multivariate subdivision. We derive sufficient conditions for convergence and optimality

From playlist Numerical Analysis and Scientific Computing

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Paul Kotyczka: Discrete-time port-Hamiltonian systems and control

CONFERENCE Recorded during the meeting "Energy-Based Modeling, Simulation, and Control of Complex Constrained Multiphysical Systems" the April 21, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other

From playlist Control Theory and Optimization

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Thomas Ransford: Constructive polynomial approximation in Banach spaces of holomorphic functions

Recording during the meeting "Interpolation in Spaces of Analytic Functions" the November 21, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio

From playlist Analysis and its Applications

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Why don't they teach Newton's calculus of 'What comes next?'

Another long one. Obviously not for the faint of heart :) Anyway, this one is about the beautiful discrete counterpart of calculus, the calculus of sequences or the calculus of differences. Pretty much like in Alice's Wonderland things are strangely familiar and yet very different in this

From playlist Recent videos

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Adeline Roux-Langlois : Using structured variants in lattice-based cryptography - Lecture 1

CONFERENCE Recording during the thematic meeting : « Francophone Computer Algebra Days» the March 06, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIRM's Audiov

From playlist Mathematical Aspects of Computer Science

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Minimax Approximation and the Exchange Algorithm

In this video we'll discuss minimax approximation. This is a method of approximating functions by minimisation of the infinity (uniform) norm. The exchange algorithm is an iterative method of finding the approximation which minimises the infinity norm. FAQ : How do you make these animatio

From playlist Approximation Theory

Related pages

Big O notation | Approximation algorithm | Approximation-preserving reduction | Gerhard J. Woeginger | L-reduction | APX | Randomized algorithm | PTAS reduction | Optimization problem | Fully polynomial-time approximation scheme