If I want to work polynomial like bernstein, how it can be coded to differentiate and integrate.This is defined as Bi,n=nCr(n,i)xi(1-x)n-i. If I have to calculate B2,7=nCr(7,2)x2(1-x)5=21x2(1-x)5?How to work this in matlab?
This is a good question with many possible answers.
Fortunately, Matlab has a built-in bernstein function. A sample implementation with a plot is given in
https://www.mathworks.com/help/symbolic/bernstein.html
and
https://www.mathworks.com/help/symbolic/bernsteinmatrix.html
See the attached image for sample Bernstein function plots. It is a pity that Mathworks does not write Bernstein(...) instead of bernstein(...). The Matlab code to implement a Bernstein polymial (notice the capital B) is given in
http://www.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation/content/BSFKFolder/private/Bernstein.m
More to the point, Matlab can be used to compute the derivative of a Bernstein polynomial, using the technique shown in
https://people.sc.fsu.edu/~jburkardt/m_src/bernstein_polynomial/bernstein_polynomial.html
An excellent overview of Bernstein polynomials is given in
http://mathworld.wolfram.com/BernsteinPolynomial.html
An implementation of Hermite polynomials in Matlab is given in
https://www.mathworks.com/help/symbolic/hermiteh.html
The Matlab code used to define a hermite polynomial function is given in
https://www.mathworks.com/matlabcentral/fileexchange/27746-hermite-polynomials/content/hermite.m
For a thorough look at Hermite polynomials from a Matlab perspective, see
https://www.researchgate.net/publication/265817738_Applied_numerical_methods_using_MATLAB
For the differentiation of Bernstein polynomials, see
https://www.researchgate.net/publication/228603634_A_MATLAB_differentiation_matrix_suite
Article A MATLAB differentiation matrix suite
Article Applied numerical methods using MATLAB
This is a good question with many possible answers.
Fortunately, Matlab has a built-in bernstein function. A sample implementation with a plot is given in
https://www.mathworks.com/help/symbolic/bernstein.html
and
https://www.mathworks.com/help/symbolic/bernsteinmatrix.html
See the attached image for sample Bernstein function plots. It is a pity that Mathworks does not write Bernstein(...) instead of bernstein(...). The Matlab code to implement a Bernstein polymial (notice the capital B) is given in
http://www.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation/content/BSFKFolder/private/Bernstein.m
More to the point, Matlab can be used to compute the derivative of a Bernstein polynomial, using the technique shown in
https://people.sc.fsu.edu/~jburkardt/m_src/bernstein_polynomial/bernstein_polynomial.html
An excellent overview of Bernstein polynomials is given in
http://mathworld.wolfram.com/BernsteinPolynomial.html
An implementation of Hermite polynomials in Matlab is given in
https://www.mathworks.com/help/symbolic/hermiteh.html
The Matlab code used to define a hermite polynomial function is given in
https://www.mathworks.com/matlabcentral/fileexchange/27746-hermite-polynomials/content/hermite.m
For a thorough look at Hermite polynomials from a Matlab perspective, see
https://www.researchgate.net/publication/265817738_Applied_numerical_methods_using_MATLAB
For the differentiation of Bernstein polynomials, see
https://www.researchgate.net/publication/228603634_A_MATLAB_differentiation_matrix_suite
Article A MATLAB differentiation matrix suite
Article Applied numerical methods using MATLAB
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