Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view of this problem leads to efficient preprocessing techniques, applying polyhedral methods on the exact exponents with numerical techniques on the approximate coefficients. With Maple we will illustrate our use of tropical algebraic geometry.

Since its introduction in the mid-sixties (Zadeh, L. A., (1965)), fuzzy set theory has gained recognition in a number of fields in the cases of uncertain, or qualitative or linguistically described system parameters or processes based on approximate reasoning, and has proven suitable and applicable with system describing rules of similar characteristics. It can be successfully applied with nume...

In applications such as multimedia that tolerate imprecise results, approximate computing techniques can sacrifice precision to save power or time. One aspect of approximate computing is imprecise storage in multi-level cells (MLCs). Computer words that are too large for a single MLC must be distributed across multiple approximate MLCs. The wordlevel imprecision depends on how the words are spl...

In this paper, we proposed a new low overhead collaborative technique of output quality monitoring for approximate computing on GPUs. In this technique, the CPU is responsible for performing quality monitoring while the GPU executes approximate kernels. For two image processing applications, we showed that this technique outperforms previous quality monitoring techniques.

Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral methods on the exact exponents with numerical techniques on the approximate coefficients. With Maple we will illustrate our use of tropical algebraic geometry.

An approximate root of an univariate polynomial over a graded ring A is an element in A for which the evaluated polynomial vanishes up to a prescribed order. We give an algorithm for deciding existence of approximate roots and computing essentially all of them. Based on this algorithm we also suggest a finite representation for multivariate algebraic power series.

In this paper, we consider generalized mixed co-quasi-variational inclusions and propose an iterative algorithm for computing their approximate solutions by using definition of J-proximal mapping given in [9]. We prove that the approximate solutions obtained by proposed algorithm converge to the exact solution of our co-quasi-variational inclusion. Some special cases are also discussed. AMS Sub...

Description Logics, and in particular the web ontology language OWL has been proposed as an appropriate basis for computing matches between structured objects for the sake of information integration and service discovery. A drawback of the direct use of subsumption as a matching criterion is the inability to compute partial matches and qualify the degree of mismatch. In this paper, we describe ...

Discretization algorithms for solving semi-infinite minimax problems replace the original problem by an approximation involving the maximization over a finite number of functions and then solve the resulting approximate problem. The approximate problem gives rise to a discretization error and its solution results in an optimization error as a minimizer of that problem is rarely achievable with ...