LazySets.jl: Scalable Symbolic-Numeric Set Computations$^*$

CGO: G: Decoupling Symbolic from Numeric in Sparse Matrix Computations

Sympiler is a domain-speci c code generator that optimizes sparse matrix computations by decoupling the symbolic analysis phase from the numerical manipulation stage in sparse codes. The computation patterns in sparse numerical methods are guided by the input sparsity structure and the sparse algorithm itself. In many real-world simulations, the sparsity pattern changes little or not at all. Sy...

Numeric versus Symbolic Computation

Twentyfive years ago when I studied Physics, only one of the students who participated in a laboratory course that I took was possessing one of the first calculators to process the data we were obtaining. Believe it or not, everybody else, including me, had to use a slide-rule for this purpose. Nowadays, the calculator is used by everybody, by far not only for academic purposes. Hence it is the...

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...

Robust Symbolic-Numeric-Graphic Software

Issues in the field of intelligent scientific computing are addressed from the point of view of the development of a problem solving environment. These issues include how symbolic, numeric and graphic code should be linked, how a system might be constructed so that it is robust and survives a changing environment, and whether language translators have a role in the retention of the algorithmic ...

Symbolic-Numeric Algebra for Polynomials