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Differentiation matrices for univariate polynomials.
- Source :
- Numerical Algorithms; Jan2020, Vol. 83 Issue 1, p1-31, 31p
- Publication Year :
- 2020
-
Abstract
- Differentiation matrices are in wide use in numerical algorithms, although usually studied in an ad hoc manner. We collect here in this review paper elementary properties of differentiation matrices for univariate polynomials expressed in various bases, including orthogonal polynomial bases and non-degree-graded bases such as Bernstein bases and Lagrange and Hermite interpolational bases. We give new explicit formulations, and new explicit formulations for the pseudo-inverses which help to understand antidifferentiation, of many of these matrices. We also give the unique Jordan form for these (nilpotent) matrices and a new unified formula for the transformation matrix. [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIALS
MATRICES (Mathematics)
ORTHOGONAL polynomials
Subjects
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 83
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 141253309
- Full Text :
- https://doi.org/10.1007/s11075-019-00668-z