Abstract
We give an effective method for computing the entropy for polynomials orthogonal on a segment of the real axis, which uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on a series expression for the mutual energy of two probability measures naturally connected with the polynomials. The particular case of Gegenbauer polynomials is analyzed in detail. These results are applied also to the computation of the entropy of spherical harmonics, important for the study of entropic uncertainty relations as well as the spatial complexity of physical systems in central potentials.
| Original language | English |
|---|---|
| Pages (from-to) | 488-509 |
| Number of pages | 22 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 26 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Jan 2005 |
| Externally published | Yes |
Keywords
- Entropic uncertainty relation
- Entropy
- Gegenbauer polynomials
- Jacobi matrix
- Orthogonal polynomials
- Spherical harmonics
- Three-term recurrence relation
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
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