Solving change of basis from Bernstein to Chebyshev polynomials
We provide two closed-form solutions to the change of basis from Bernstein polynomials to shifted Chebyshev polynomials of the fourth kind and show them to be equivalent by applying Zeilberger’s algorithm. The first solution uses orthogonality properties of the Chebyshev polynomials. The second is “...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-06-01
|
| Series: | Examples and Counterexamples |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X25000059 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823864242827165696 |
|---|---|
| author | D.A. Wolfram |
| author_facet | D.A. Wolfram |
| author_sort | D.A. Wolfram |
| collection | DOAJ |
| description | We provide two closed-form solutions to the change of basis from Bernstein polynomials to shifted Chebyshev polynomials of the fourth kind and show them to be equivalent by applying Zeilberger’s algorithm. The first solution uses orthogonality properties of the Chebyshev polynomials. The second is “modular” which enables separately verified sub-problems to be composed and re-used in other basis transformations. These results have applications in change of basis of orthogonal, and non-orthogonal polynomials. |
| format | Article |
| id | doaj-art-681f91cf54b94db4a434cd72f223394e |
| institution | Kabale University |
| issn | 2666-657X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj-art-681f91cf54b94db4a434cd72f223394e2025-02-09T05:01:32ZengElsevierExamples and Counterexamples2666-657X2025-06-017100178Solving change of basis from Bernstein to Chebyshev polynomialsD.A. Wolfram0ANU College of Systems and Society, Australian National University, Canberra, ACT 0200, AustraliaWe provide two closed-form solutions to the change of basis from Bernstein polynomials to shifted Chebyshev polynomials of the fourth kind and show them to be equivalent by applying Zeilberger’s algorithm. The first solution uses orthogonality properties of the Chebyshev polynomials. The second is “modular” which enables separately verified sub-problems to be composed and re-used in other basis transformations. These results have applications in change of basis of orthogonal, and non-orthogonal polynomials.http://www.sciencedirect.com/science/article/pii/S2666657X25000059Polynomial basisChange of basisConnection formula |
| spellingShingle | D.A. Wolfram Solving change of basis from Bernstein to Chebyshev polynomials Examples and Counterexamples Polynomial basis Change of basis Connection formula |
| title | Solving change of basis from Bernstein to Chebyshev polynomials |
| title_full | Solving change of basis from Bernstein to Chebyshev polynomials |
| title_fullStr | Solving change of basis from Bernstein to Chebyshev polynomials |
| title_full_unstemmed | Solving change of basis from Bernstein to Chebyshev polynomials |
| title_short | Solving change of basis from Bernstein to Chebyshev polynomials |
| title_sort | solving change of basis from bernstein to chebyshev polynomials |
| topic | Polynomial basis Change of basis Connection formula |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X25000059 |
| work_keys_str_mv | AT dawolfram solvingchangeofbasisfrombernsteintochebyshevpolynomials |