Orthonormal Polynomials under Different Inner Product Measures

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows how the orthonormal polynomials of a space where the inner product is a weighted integral vary with the weight function , . Here, the monomial basis is orthonormalized by the Gram–Schmidt process with respect to the inner product and the weight functions are probability measures (so that ) corresponding to the Legendre, Hermite, Laguerre and generalized Laguerre polynomials.

Contributed by: Celestine Preetham Lawrence (August 2022)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The variable is often time [1].

Reference

[1] A. Gu, T. Dao, S. Ermon, A. Rudra and C. Re, "Hippo: Recurrent Memory with Optimal Polynomial Projections," Advances in Neural Information Processing Systems, 33, 2020 pp. 1474–1487. par.nsf.gov/biblio/10214620.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send