Polinomi di Bernstein

[gimpaolo]

Qualcuno mi sa dire quale relazione esiste tra i polinomi di
Bernstein e le matrici di Pascal?
Ciao da Giampaolo

[Cavia1]

Sul numero di marzo 2001 dell'American Mathematical Monthly è apparso un articolo sull'argomento da parte di due matematici italiani. Penso che tu possa contattarli personalmente (ti ho indicato i loro indirizzi e-mail)


The Matrices of Pascal and other Greats
by Lidia Aceto and Donato Trigiante
[e-mail]
[e-mail]
Historical references to the Pascal matrix go back to the fourteenth century. It is mentioned in an ancient book of Chinese mathematics. Its many properties continue to surprise also for the variety of its applications in such diverse fields as probability, numerical analysis, surface reconstruction, and combinatorics. Recent studies of its properties have taken new directions, which highlight its relations with other important matrices. In this paper such connections are studied in a deeper way, establishing the relations existing between the Pascal matrix and some families of classical polynomials. For example, the Bernstein matrix Be(x), whose entries are the Bernstein polynomials, can be written in the very simple form


Be(x) = P D(x) inv (P),

where D(x) is a diagonal matrix and P is the Pascal matrix.

Cavia