TNC'18:Papers with AbstractsPapers 

Abstract. In this paper, we propose a modified policy iterations algorithm which does not rely on the selection property. The selection property is the key argument to make improvements during policy iterations. Indeed, a new policy is computed as an optimal solution of a minimization problem. However, in some cases, it might be difficult to prove that an optimal solution exists. To overcome this issue, the new policy is computed as a guaranteed suboptimal solution of the minimization problem. The good choice of the perturbation parameters preserves the advantages of the original policy iterations algorithm such as the computation of a postfixed point at each step and the convergence to a fixed point.  Abstract. In high performance computing, nearly all the implementations and published experiments use floatingpoint arithmetic. However, since floatingpoint numbers are finite approximations of real numbers, it may result in hazards because of the accumulated errors. These roundoff errors may cause damages whose gravity varies depending on the critical level of the application. To deal with this issue, we have developed a tool which im proves the numerical accuracy of computations by automatically transforming programs in a sourcetosource manner. Our transformation, relies on static analysis by abstract interpretation and operates on pieces of code with assignments, conditionals, loops, functions and arrays. In this article, we apply our techniques to optimize a parallel program representative of the high performance computing domain. Parallelism introduces new numerical accuracy problems due to the order of operations in this kind of systems. We are also interested in studying the compromise between execution time and numerical accuracy.  Abstract. The purpose of this talk is primarily to introduce a new methodology to synthesize numerically accurate programs for the Gaussian elimination method in order to solve linear systems coming from mechanical problems. The synthesis is based on program transformation techniques and it is guided in its estimation of accuracy by interval arithmetic that computes the propagation of roundoff errors. Besides a discussion on numerical accuracy issues related to floatingpoints arithmetics and roundoff errors, we present our approach used to compute the error bound during the resolution process. Finally, some experimental results will be presented to prove the efficiency of our synthesizer tool and show that the specialized produced code to solve the family of systems given in input is far more accurate and faster than the standard implementation of the Gauss method.  Abstract. Discrete Stochastic Arithmetic (DSA) enables one to estimate rounding errors and to detect numerical instabilities in simulation programs. DSA is implemented in the CADNA library that can analyze the numerical quality of single and double precision programs. In this article, we show how the CADNA library has been improved to enable the estimation of rounding errors in programs using quadruple precision floatingpoint variables, i.e. having 113bit mantissa length. Although an implementation of DSA called SAM exists for arbitrary precision programs, a significant performance improvement has been obtained with CADNA compared to SAM for the numerical validation of programs with 113bit mantissa length variables. This new version of CADNA has been successfully used for the control of accuracy in quadruple precision applications, such as a chaotic sequence and the computation of multiple roots of polynomials. We also describe a new version of the PROMISE tool, based on CADNA, that aimed at reducing in numerical programs the number of double precision variable declarations in favor of single precision ones, taking into account a requested accuracy of the results. The new version of PROMISE can now provide type declarations mixing single, double and quadruple precision.  Abstract. In this paper we deal with detection of unsolvability of interval linear systems. Various methods based on existing algorithms or on existing sufficient conditions are developed. The methods are tested on a large variety of random systems and the results are visualized. The two strongest sufficient conditions are proved to be equivalent under a certain assumption. The topic of detecting solvability is also touched upon.  Abstract. Solving systems of parametric linear equations with parameters varying within closed intervals is a hard computational problem. However, we may reduce the problem dimension and thus make the problem more tractable by utilizing the monotonicity of the solution components with respect to the parameters. In this paper, we propose two improvements of the standard monotonicity checking techniques. The first improvement relies on creating a system with original variables and their derivatives as unknowns, and the second one employs the socalled psolution. By a series of numerical experiments we show that the improved monotonicity approach outperforms the standard one. 

