Hello Everybody!
I am trying to comprehend the underlying theory of orthogonal polynomials in the context of Gaussian quadrature formulae; the abscissas in the N-point quadrature formula are the N-roots (or zeros) of a polynomial orthogonal with respect to the weight function.
So, one needs to evaluate the family of orthogonal polynomials corresponding to an arbitrary weight function. Gram Schmidt algorithm can be used to generate these orthogonal polynomials starting from a set of linearly independent monomials (1, x, x^2, x^3,.....). A more simpler way is to make use of a three term recurrence formula; I am seeking suggestions to gather easy-to-grasp material (as I lack adequate background in this area) that helps me to understand how this recurrence formula is derived and how it is normalized? and how one can figure out if a given recurrence formula is normalized or not.
Thanks in advance!
KD
My book, The Many Uses of Orthogonal Functions, is free today (8/26) https://www.amazon.com/dp/B07GT8TLDV I also discuss this in Numerical Calculus, which will be free on 9/14. You can download the software free here http://dudleybenton.altervista.org/software/index.html So what do you hope to do with this? Perhaps I can help. I have tons of free software.
Thanks very much, Sir; I figured out my queries. I had a brief look at your page and it's mind blowing. I believe that I just found an excellent source to learn various concepts from in application point of view. I am trying to understand and apply the quadrature-based moment techniques to solve a population balance equation in the context of gas-solid flows; evaluation of weights and abscissas is at the heart of these techniques and the theory of orthogonal functions, as I understand, greatly simplifies this effort.
Thanks and Regards,
Kareem
I'm always glad to help. Be sure to keep us posted on your progress.
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