𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Efficient evaluation of polynomial forms

✍ 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.

✦ 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.


πŸ“œ SIMILAR VOLUMES


Symmetric multilinear forms and polariza
✍ AleΕ‘ DrΓ‘pal; Petr VojtΔ›chovskΓ½ πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 229 KB

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

Evaluations of the Circuit Partition Pol
✍ BΓ©la BollobΓ‘s πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 88 KB

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