Search

Injective parametrizations are widely used both in theory and in applications. The injectivity of parameteric curves and surfaces means that there are no self-intersections. Toric surface patch is defined by a set of integer lattice points A and corresponding control points and weights, which includes rational tensor product and triangle Bézier patches as special cases. In 2011, Sottile and Zhu presented a geometric method to check the injectivity of 2D toric surface patches. In this paper, we present an improved algorithm of their method. The complexity of the improved algorithm is reduced from O (n 3) to O (n 2) , where n = # (A). Some examples are shown to illustrate the effectiveness of our algorithm. Moreover, the algorithm is also applied to check the injectivity of parameterization in isogeometric analysis. [ABSTRACT FROM AUTHOR]

Abstract: Constrained matrix games with payoffs of triangular fuzzy numbers (TFNs) are a type of matrix games with payoffs expressed by TFNs and sets of players’ strategies which are constrained. So far as we know, no study have yet been attempted for constrained matrix games with payoffs of TFNs since there is no effective way to simultaneously incorporate the payoffs’ fuzziness and strategies’ constraints into classical and/or fuzzy matrix game methods. The aim of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of TFNs. In this methodology, we introduce the concepts of Alpha-constrained matrix games for constrained matrix games with payoffs of TFNs and the values. By the duality theorem of linear programming, it is proven that players’ gain-floor and loss-ceiling always have a common interval-type value and hereby any Alpha-constrained matrix game has an interval-type value. Moreover, using the representation theorem for the fuzzy set, it is proven that any constrained matrix game with payoffs of TFNs always has a TFN-type fuzzy value. The auxiliary linear programming models are derived to compute the lower and upper bounds of the interval-type value and optimal strategies of players for any Alpha-constrained matrix game. In particular, the mean and the lower and upper limits of the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs can be directly obtained through solving the derived three linear programming models with data taken from only 1-cut and 0-cut of payoffs. Hereby the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs are easily computed. The proposed method in this paper is compared with other methods and its validity and applicability are illustrated with a numerical example. [Copyright &y& Elsevier]

This paper presents the development of parallel algebraic multigrid solvers on NVIDIA GPUs. A classical algebraic multigrid solver and a smoothed aggregation algebraic multigrid solver are implemented. The W-cycle, F-cycle and V-cycle are investigated. Various coarsening strategies and interpolation operators are implemented. A group of smoothers are also provided. Numerical experiments show that the solution phase of our GPU-based algebraic solvers is up to 13 times faster than that of the sequential CPU-based algebraic multigrid solvers on our workstation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the properties of regular systems and improve the efficiency of the regular decomposition method RegSer implemented in Epsilon. We define a weaker concept which retains most properties of regular system. It can be shown that from a weak regular system one can also define a regular set and vice versa. We present an algorithm RecurWeakRegSer to decompose a given polynomial system into weak regular systems. When , the output of RecurWeakRegSer() often contains fewer components than that of RegSer(). This is one advantage of RecurWeakRegSer. Another one is that RecurWeakRegSer is more efficient than RegSer. This was shown by experiments that we carried out. Since it is an essential step in RegSer to compute subresultant polynomial remainder sequences (PRS), and there is some weakness in the implementation, we implement a new version of subresultant algorithm using the optimization strategy of Ducos so that the efficiency of RegSer can be improved. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the behavioral pseudometrics for probabilistic systems, which are a quantitative analogue of probabilistic bisimilarity in the sense that the distance zero captures the probabilistic bisimilarity. The model we are interested in is probabilistic automata, which are based on state transition systems and make a clear distinction between probabilistic and nondeterministic choices. The pseudometrics are defined as the greatest fixpoint of a monotonic functional on the complete lattice of state metrics. A distinguished characteristic of this pseudometric lies in that it does not discount the future, which addresses some algorithmic challenges to compute the distance of two states in the model. We solve this problem by providing an approximation algorithm: up to any desired degree of accuracy , the distance can be approximated to within in time exponential in the size of the model and logarithmic in . One of the key ingredients of our algorithm is to express a pseudometric being a post-fixpoint as the elementary sentence over real closed fields, which allows us to exploit Tarski’s decision procedure, together with the binary search to approximate the behavioral distance. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and study completely generalized multivalued nonlinear co-quasi-variational-like inclusions. By using J η-proximal mapping [1], we propose an iterative algorithm for computing the approximate solutions of completely generalized multivalued nonlinear co-quasi-variational-like inclusions problem. We prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of completely generalized multivalued nonlinear co-quasi-variational-like inclusions problem. Some special cases are also discussed. [Copyright &y& Elsevier]

Abstract: One of the main problems dealing with iterative methods for solving polynomial systemsis the initialization of the iteration. This paper provides an algorithm to initialize the search of solutions of polynomial systems. [Copyright &y& Elsevier]

Abstract: In this paper, we propose an algorithm for solving the obstacle problem. We try tofind the approximated region of the contact in the obstacle problem by iteration. Numerical examples are given for the obstacle problem for a membrane and the elastic-plastic torsion problem. [Copyright &y& Elsevier]

In this paper, we introduce a new algorithm for sign detection in a residue number system, which can be applied to any number of moduli set. This technique is faster than most competitive published works, based on MRC or CRT. The CRT requires large modulo M and is therefore costly to implement. The mix radix conversion (MRC) is a sequential process which causes long delay. The proposed algorithm is based on CRT 11. No big modulo M = Πi=1pin pi operations are needed for the CRT II. The modulo multipliers in the CRT II are bounded by size √M. The new sign detector uses less hardware than previous techniques. Using the new moduli set (2, 2n − 1, 2n + 2n−1 − 1, 2n+1 + 2n − 1), the implementation of a sign detector is further simplified. [Copyright &y& Elsevier]

A multiplier-free residue to binary converter architecture based on the Chinese remainder theorem II (CRT II) [1] is presented. The paper also includes a binary to residue converter. This is achieved by introducing a new moduli set (2, 2n − 1, 2n + 2n−1 − 1, 2n+1 + 2n − 1) for RNS application. The complexity of conversion has been greatly reduced using CRT II with the new moduli set. The proposed hardware architecture replaces the necessary multiplication by shift-left operations. A similar hardware architecture is presented for the binary to residue conversion. [Copyright &y& Elsevier]

In this paper, lower and upper bounds for min-max pair heap construction has been presented. It has been shown that the construction of a min-max pair heap with n elements requires at least 2.07n element comparisons. A new algorithm for creating min-max pair heap has been devised that lowers the upper bound to 2.43n. [Copyright &y& Elsevier]