A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton–Picard Method

A symbolic-numeric silhouette algorithm

We have revisited the silhouette algorithm developed by Canny, and designed its new symbolic-numeric version. The symbolic-numeric silhouette algorithm do not require the symbolic computation of the determinants of resultant matrices, and can work on oating point arithmetic. Though its combinatorial complexity remains the same, but its algebraic complexity has been improved signi cantly which i...

A symbolic-numeric algorithm for genus computation

The genus computation problem is a classical subject in computer algebra. Presently, several symbolic algorithms are available for computing the genus of plane algebraic curves over an algebraically closed field, see [16, 18, 31]. There exist also good implementations for these algorithms in several packages of some well-known computer algebra systems such as: Maple, Magma, Singular, Axiom. We ...

Symbolic-Numeric Algebra for Polynomials

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

synaps, a library for symbolic-numeric computation

The need to combine symbolic and numeric computations is ubiquitous in many problems. Starting with an exact description of the equations, in most cases, we will eventually have to compute an approximation of the solutions. Even more, in many problems the coefficients of the equations may only be known with some inaccuracy (due, for instance, to measurement errors). In this case, we are not dea...