Remarks on piecewise-linear algebra

Remarks on Piecewise-linear Algebra

Introduction* A function f: V —>W between real vector spaces is piecewise-linear (PL) if there exists a partition of V into "open polyhedra" X€ (i.e., relative interiors of polyhedra) such that / is affine on each Xt. (As distinct to the case of PL-topology, no continuity is required of /.) Images and preimages under PL-maps give rise to finite unions of open polyhedra, or PL-seίs; conversely P...

Remarks on Piecewise Polynomial Approximation

The theoretical and experimental background for the approximation of "real-world" functions is reviewed to motivate the use of piecewise polynomial approximations. It is possible in practice ~o achieve the results suggested by the theory for piecewise polynomials. A convergent adaptive algorithm is outlined which effectively and efficiently computes smooth piecewise polynomial approxImations to...

On Piecewise - Linear

If two sets of vectors (in Classification

Some Introductory Remarks on Computer Algebra

Computer algebra is a relatively young but rapidly growing field. In this introductory note to the mini-symposium on computer algebra organized as part of the third European Congress of Mathematics I will not even attempt to adress all major streams of research and the many applications of computer algebra. I will concentrate on a few aspects, mostly from a mathematical point of view, and I wil...

Piecewise Constant Controlled Linear Fuzzy Systems