In many fields of science and engineering, it is needed to find all solutions of mixed trigonometric polynomial systems. Commonly, mixed trigonometric polynomial systems are transformed into polynomial systems by vari...In many fields of science and engineering, it is needed to find all solutions of mixed trigonometric polynomial systems. Commonly, mixed trigonometric polynomial systems are transformed into polynomial systems by variable substitution and adding some quadratic equations, and then solved by some numerical methods. However, transformation of a mixed trigonometric polynomial system into a polynomial system will increase the dimension of the system and hence induces extra computational work. In this paper, we consider to solve the mixed trigonometric polynomial. systems by homotopy method directly. Homotopy with the start system constructed by GBQ-algorithm is presented and homotopy theorems are proved. Preliminary numerical results show that our constructed direct homotopy method is more efficient than the existent direct homotopy methods.展开更多
In certain computational systems the amount of space required to execute an algorithm is even more restrictive than the corresponding time necessary for solution of a problem. In this paper an algorithm for modular mu...In certain computational systems the amount of space required to execute an algorithm is even more restrictive than the corresponding time necessary for solution of a problem. In this paper an algorithm for modular multiplicative inverse is introduced and its computational space complexity is analyzed. A tight upper bound for bit storage required for execution of the algorithm is provided. It is demonstrated that for range of numbers used in public-key encryption systems, the size of bit storage does not exceed a 2K-bit threshold in the worst-case. This feature of the Enhanced-Euclid algorithm allows designing special-purpose hardware for its implementation as a subroutine in communication-secure wireless devices.展开更多
Predictor-corrector algorithm for linear programming, proposed by Mizuno et al.([1]), becomes the best well known in the interior point methods. The purpose of this paper is to extend these results in two directions. ...Predictor-corrector algorithm for linear programming, proposed by Mizuno et al.([1]), becomes the best well known in the interior point methods. The purpose of this paper is to extend these results in two directions. First, we modify the algorithm in order to solve convex quadratic programming with upper bounds. Second, we replace the corrector step with an iteration of Monteiro and Adler's algorithm([2]). With these modifications, the duality gap is reduced by a constant factor after each corrector step for convex quadratic programming. It is shown that the new algorithm has a O(root nL)-iteration complexity.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1110106711171051)the Fundamental Research Funds for the Central Universities(Grant No.DUT16LK04)
文摘In many fields of science and engineering, it is needed to find all solutions of mixed trigonometric polynomial systems. Commonly, mixed trigonometric polynomial systems are transformed into polynomial systems by variable substitution and adding some quadratic equations, and then solved by some numerical methods. However, transformation of a mixed trigonometric polynomial system into a polynomial system will increase the dimension of the system and hence induces extra computational work. In this paper, we consider to solve the mixed trigonometric polynomial. systems by homotopy method directly. Homotopy with the start system constructed by GBQ-algorithm is presented and homotopy theorems are proved. Preliminary numerical results show that our constructed direct homotopy method is more efficient than the existent direct homotopy methods.
文摘In certain computational systems the amount of space required to execute an algorithm is even more restrictive than the corresponding time necessary for solution of a problem. In this paper an algorithm for modular multiplicative inverse is introduced and its computational space complexity is analyzed. A tight upper bound for bit storage required for execution of the algorithm is provided. It is demonstrated that for range of numbers used in public-key encryption systems, the size of bit storage does not exceed a 2K-bit threshold in the worst-case. This feature of the Enhanced-Euclid algorithm allows designing special-purpose hardware for its implementation as a subroutine in communication-secure wireless devices.
文摘Predictor-corrector algorithm for linear programming, proposed by Mizuno et al.([1]), becomes the best well known in the interior point methods. The purpose of this paper is to extend these results in two directions. First, we modify the algorithm in order to solve convex quadratic programming with upper bounds. Second, we replace the corrector step with an iteration of Monteiro and Adler's algorithm([2]). With these modifications, the duality gap is reduced by a constant factor after each corrector step for convex quadratic programming. It is shown that the new algorithm has a O(root nL)-iteration complexity.
基金Supported by the National Natural Science Foundation of China under Grant No.60473130(国家自然科学基金)the National Basic Research Program of China under Grant No.2004CB318000(国家重点基础研究发展计划(973))
