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CONTENT SUMMARY: pg 1: @00:08 Introduction review; polynomials of degree 3; Lagrange, Chebyshev, Bernstein, spread polynomials; basis: standard/power, factorial, Taylor; Lagrange polynomials develope…
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More Bases of Polynomial Spaces - Lecture 21
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- 1 CONTENT SUMMARY: pg 1: @00:08 Introduction review; polynomials of degree 3; Lagrange, Chebyshev, Bernstein, spread polynomials; basis: standard/power, factorial, Taylor; Lagrange polynomials develope…
- 2 pg 2: @ Lagrange development continued; evaluation mapping;
- 3 pg 3: @ Lagrange development continued; polynomials that map to the standard basis vectors e1,e2,e3,34 Lagrange interpolation polynomials;
- 4 pg 4: @ Lagrange basis; Polynomial that goes through four desired points;
- 5 pg 5: @ Uniform approximation and Bernstein polynomials
- 6 pg 6: @ reference to Pascal's triangle; Bernstein polynomials named; Bernstein basis;
- 7 pg 7: @ view of Bernstein polynomials;
- 8 pg 8: @ Show that Bernstein polynomials of a certain degree do form a basis for that corresponding polynomial space; Pascal's triangle; Unnormalized Bernstein polynomials; WLA21_pg8_theorem Bernstein…
- 9 pg 9: @ How Bernstein polynomials are used to approximate a given continuous function on an interval;
- 10 pg 10: @ Chebyshev polynomials; using a recursive definition; Chebyshev polynomial diagram;
- 11 pg 14: @36:56 Spread polynomials relation to Chebyshevs; Spread polynomials advantage over Chebyshev; Pascal's array; Spread polynomials as a source of study @;
- 12 pg 15: @39:43 Spread basis; change of basis matrices; moral @ ;
- 13 pg 16: @ exercises 21.1-4 ;
- 14 pg 17: @43:44 exercises 21.5-7 ; closing remarks @ THANKS to EmptySpaceEnterprise
- 15 Introduction
- 16 Lagrange polynomials
- 17 Lagrange basis
- 18 Uniform approximation and Bernstein polynomials
- 19 How are Bernstein polynomials used?
- 20 Chebyshev polynomials
- 21 Chebyshev basis
- 22 Chebyshev polynomials in approximation and integration theories
- 23 Relation between Spread and Chebyshev polys
- 24 Spread basis
