Discrete Integration and Derivation
1999 (English)Conference paper (Refereed)
This paper introduces a computational framework - termeddiscrete integration-which presents an algebraic interpretation of integration that captures the combinatorialaspects of the fundamental theorem of calculus at a finite level. This facilitatesdiscrete approximations of integrals that are evaluated over smooth geometric configurations,since it enables their numerical approximation within the same conceptualspace. It also makes possible a discrete version of the differential and integral calculusover various function classes. We illustrate these ideas in the case of polynomial functions- establishing a scale-invariant way to compute with sums of polynomialsdefined on simplexes1.
Place, publisher, year, edition, pages
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-82645OAI: oai:DiVA.org:kth-82645DiVA: diva2:498426
The 5:th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa-Zihuatanejo
NR 201408052012-02-122012-02-12Bibliographically approved