Theorems in approximation theory
In approximation theory, Bernstein's theorem is a converse to Jackson's theorem. The first results of this type were proved by Sergei Bernstein in 1912. For approximation by trigonometric polynomials, the result is as follows: Let f: [0, 2π] → C be a 2π-periodic function, and assume r is a natural number, and 0 < α < 1. If there exists a number C(f) > 0 and a sequence of trigonometric polynomials {Pn}n ≥ n0 such that then f = Pn0 + φ, where φ has a bounded r-th derivative which is α-Hölder continuous. (Wikipedia).
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
Seminar on Applied Geometry and Algebra (SIAM SAGA): Frank Sottile
Date: Tuesday, August 10 Speaker: Frank Sottile, Texas A&M Title: Applications of Bernstein's Other Theorem Abstract: Many of us are familiar with Bernstein's Theorem giving the number of solutions in the torus to a general system of sparse polynomial equations. The linchpin of his proo
From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)
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
Mod-01 Lec-02 Polynomial Approximation
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
Approximating Functions in a Metric Space
Approximations are common in many areas of mathematics from Taylor series to machine learning. In this video, we will define what is meant by a best approximation and prove that a best approximation exists in a metric space. Chapters 0:00 - Examples of Approximation 0:46 - Best Aproximati
From playlist Approximation Theory
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
Alexander Pushnitski : Rational approximation of functions with logarithmic singularities
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 Analysis and its Applications
Nigel Higson: Isomorphism conjectures for non discrete groups
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" I shall discuss aspects of the C*-algebraic version of the Farrell-Jones conjecture (namely the Baum-Connes conjecture) for Lie groups and p-adic groups. The conj
From playlist HIM Lectures: Junior Trimester Program "Topology"
The Bernstein Sato polynomial: Bernstein's inequality
This is the second of three talks about the Bernstein-Sato polynomial. The first talk is at https://youtu.be/CX2iej9NKzs The third talk should appear at https://youtu.be/3FLdcrbUXZw on Dec 23 5:00am PST We study the Weyl algebra of differential operators with polynomial coefficients in
From playlist Commutative algebra
Bernard teissier: Another type of approximation: the valuative Cohen theorem
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 Algebraic and Complex Geometry
The Bernstein Sato polynomial: Introduction
This is the first of three talks about the Bernstein-Sato polynomial. The second talk should appear at https://youtu.be/FAKzbvDm-w0 on Dec 22 5:00am PST We define the Bernstein-Sato polynomial of a polynomial in several complex variables, and show how it can be used to analytically con
From playlist Commutative algebra
MAST30026 Lecture 17: Integrals
I began by explaining how, in order to work with infinite-dimensional function spaces constructively, we need to use integrals. Then I defined an "integral pair", showed that the Riemann integral on a closed interval is an example, and proved that there is a product operation on integral p
From playlist MAST30026 Metric and Hilbert spaces
MAST30026 Lecture 16: Stone-Weierstrass theorem (Part 1)
The Weierstrass approximation theorem says that an arbitrary continuous function on a finite closed interval can be approximated uniformly by polynomials to any desired degree of accuracy. I proved this theorem using Bernstein polynomials. Lecture notes: http://therisingsea.org/notes/mas
From playlist MAST30026 Metric and Hilbert spaces
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
8ECM Invited Lecture: Albert Cohen
From playlist 8ECM Invited Lectures
Wim Veys : Zeta functions and monodromy
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 Number Theory
Hajar Bahouri - De l'analyse des EDPs non linéaires à la théorie des groupes
Créteil, Prix Paul Doisteau 2016 Réalisation technique : Antoine Orlandi (GRICAD) | Tous droits réservés
From playlist Des mathématiciens primés par l'Académie des Sciences 2017
Taylor polynomials -- 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