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Maple worksheets on Bernstein polynomials and polynomial approximation |
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Approximation of functions:
- Taylor Series
- Fourier Series
- Convergence of Fourier Series
- Bernstein polynomials and polynomial approximation
The following Maple worksheets can be downloaded.
They are all compatible with Classic Worksheet Maple 10.
BEZIER CURVE
Bezier curves and Bernstein polynomials - bezier.mws
- Introduction
- Quadratic Bezier curves
- Cubic Bezier curves
- General Bezier curves and Bernstein polynomials
- An animation procedure for Bezier curves and Bernstein polynomials: bezier.
The Bernstein basis polynomials and de Casteljau's algorithm - casteljau.mws
- Bernstein basis polynomials
- A recursive definition of the Bernstein polynomials
- An inductive proof that the Bernstein polynomials form a partition of unity
- de Casteljau's algorithm
- A procedure implementing de Casteljau's algorithm: casteljau.
Bernstein polynomials associated with powers of x - brnpower.mws
- Bernstein polynomials for 1
- Bernstein polynomials for x
- Bernstein polynomials for x-x^2
- Bernstein polynomials for x^2
- Bernstein polynomials for x-x^3
- Bernstein polynomials for x^3
- Summary
The Bernstein polynomials as a basis for polynomials - brnbasis.mws
- The degree raising formula
- Expressing a power x^k as a linear combination of Bernstein polynomials
- The Bernstein polynomials as a basis
- Matrices for the change of basis
- The Bernstein coefficients of the Bernstein polynomial associated with a polynomial function
The Weierstrass polynomial approximation theorem - weierstrass.mws
- The Weierstrass theorem
- Reduction to continuous functions on [0,1]
- The modulus of continuity of a continuous functions on [0,1]
- A constructive proof of the Weierstrass theorem based on Bernstein polynomials
Approximation of functions using partitions of unity - partunit.mws
- Introduction - Bernstein polynomials
- Approximation using rectangular pulses
- Approximation using "bell-shaped" pulses"
- Approximation using wider "bell-shaped" pulses"
More examples of partitions of unity - partunit2.mws
- Approximation using "bell-shaped" pulses" - II
- Approximation using wider "bell-shaped" pulses" - II
Examples of Bernstein polynomials on [-1,1] - brnexamp.mws
Comparison of polynomial approximations - polyapprox.mws
- Introduction
- Taylor polynomials
- Legendre polynomials
- Bernstein polynomials
- Summary
Function approximation procedures - fcnapprx.zip
BEZIER BASIS POLYNOMIALS
