Efficient evaluation of polynomial forms
β Scribed by Ian Munro; Allan Borodin
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 614 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0022-0000
No coin nor oath required. For personal study only.
β¦ Synopsis
The evaluation of several polynomial forms is considered. New algorithms for the evaluation of a polynomial and its derivative, a polynomial at two points, a polynomial of high degree using multiple precision arithmetic, and a bivariate polynomial of the form ~a(i)xiy "-i are presented. Various "coefficient splitting techniques" are introduced in these algorithms and the optimality of certain techniques is shown.
π SIMILAR VOLUMES
We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in n variables. The main tool is combinatorial polarization, and the approach is applicable even when n! is not invertible in the un
used Hopf algebra techniques to prove some beautiful combinatorial interpretations of the Martin polynomial for unoriented graphs. Our aim here is to give very simple proofs of similar interpretations for a considerably wider class of values. The results look particularly simple when formulated for