A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can ...A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can easily be got by directly solving linear matrixequations rather than structure motion differential equations. Moreover, in order to solve thecorresponding linear matrix equations, the numerical integration fast algorithm is presented. Thenaccording to the results, dynamic design and life-span estimation can be done. Besides, the newalgorithm can solve non-proportion damp structure response.展开更多
The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal de...The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.展开更多
In this paper we proposed an AMH Supply Chain model to obtain optimal solutions for Two-, Three- and Four-Stage for deterministic models. Besides deriving its algebraic solutions, a simple searching method is successf...In this paper we proposed an AMH Supply Chain model to obtain optimal solutions for Two-, Three- and Four-Stage for deterministic models. Besides deriving its algebraic solutions, a simple searching method is successfully applied in obtaining optimal total costs and its integer multipliers. Our model has shown promising results in comparison to Equal Cycle Time and other existing ones. The tests focused on obtaining optimal total annual costs and other related details of Two-, Three- and Four-Stage for deterministic models. The results are run under Visual Basic Programming platform using Intel? CoreTM2 Duo T6500 Processor.展开更多
The desire to increase spatial and temporal resolution in modeling groundwater system has led to the requirement for intensive computational ability and large memory space. In the course of satisfying such requirement...The desire to increase spatial and temporal resolution in modeling groundwater system has led to the requirement for intensive computational ability and large memory space. In the course of satisfying such requirement, parallel computing has played a core role over the past several decades. This paper reviews the parallel algebraic linear solution methods and the parallel implementation technologies for groundwater simulation. This work is carried out to provide guidance to enable modelers of groundwater systems to make sensible choices when developing solution methods based upon the current state of knowledge in parallel computing.展开更多
In this paper, a parallel simulation algorithm for the control problem in differential algebraic system is presented. The error of the algorithm is estimated. The stability analysis is made for a model problem and the...In this paper, a parallel simulation algorithm for the control problem in differential algebraic system is presented. The error of the algorithm is estimated. The stability analysis is made for a model problem and the stability region is given. The numerical example demonstrates that the method is efficient.展开更多
The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decis...The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decision diagram (ADD) or variants thereof provides canonical forms to represent and manipulate Boolean functions and pseudo-Boolean functions efficiently. ADD and OBDD-based symbolic algorithms give improved results for large-scale combinatorial optimization problems by searching nodes and edges implicitly. We present novel symbolic ADD formulation and algorithm for maximum weighted matching in bipartite graphs. The symbolic algorithm implements the Hungarian algorithm in the context of ADD and OBDD formulation and manipulations. It begins by setting feasible labelings of nodes and then iterates through a sequence of phases. Each phase is divided into two stages. The first stage is building equality bipartite graphs, and the second one is finding maximum cardinality matching in equality bipartite graph. The second stage iterates through the following steps: greedily searching initial matching, building layered network, backward traversing node-disjoint augmenting paths, updating cardinality matching and building residual network. The symbolic algorithm does not require explicit enumeration of the nodes and edges, and therefore can handle many complex executions in each step. Simulation experiments indicate that symbolic algorithm is competitive with traditional algorithms.展开更多
How to verify that a given fuzzy set A∈F(X *) is a fuzzy code? In this paper, an algorithm of test has been introduced and studied with the example of test. The measure notion for a fuzzy code and a precise form...How to verify that a given fuzzy set A∈F(X *) is a fuzzy code? In this paper, an algorithm of test has been introduced and studied with the example of test. The measure notion for a fuzzy code and a precise formulation of fuzzy codes and words have been discussed. sification:90K20,94D05.展开更多
A class of parallel Rosenbrock methods for differential algebraic equations are presented in this paper. The local truncation errors are defined and the order conditions are established by using the DA-trees and DA-se...A class of parallel Rosenbrock methods for differential algebraic equations are presented in this paper. The local truncation errors are defined and the order conditions are established by using the DA-trees and DA-series. The paper also deals with the convergence of the parallel Rosenbrock methods for h -> 0 and states the bounds for the global errors of the methods. Some particular methods are obtained by solving the order equations and a numerical example is given, from which the theoretical orders are actually observed.展开更多
It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used suc...It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used successfully to improve the image quality. This paper studies the application of iterative algorithms in radar imaging. A discrete model is first derived, and the iterative algorithms are then adapted to radar imaging. Although such algorithms are usually time consuming, this paper shows that, if the algorithms are appropriately simplified, it is possible to realize them even in real time. The efficiency of iterative algorithms is shown through computer simulations.展开更多
Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosen...Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosenbrock methods are effective. Applying the methods, a fast and high-precision numerical algorithm is given to deal with typical discontinuous parts, which occur frequently in differential-algebraic systems(DAS).展开更多
Suppose C is an irreducible algebraic curve of genus g, C*(D,G) is an algebraic geometric code with designed minimum distance d* = deg(G)-2g + 2. In this paper, a decoding algorithm based on Fundamental Iterative Algo...Suppose C is an irreducible algebraic curve of genus g, C*(D,G) is an algebraic geometric code with designed minimum distance d* = deg(G)-2g + 2. In this paper, a decoding algorithm based on Fundamental Iterative Algorithm(FIA) is presented, also its reasonableness is proved. In fact, our decoding algorithm is a modification of the algorithm proposed by G. L. Fend and T. R. N. Rao(1993) and can correct any received words with errors not more than (d*-1)/2, whereas the complexity is only about one half as much as Feng and Rao’s. The procedure can be implemented easily by hardware or software.展开更多
In the current paper, the authors present a symbolic algorithm for solving doubly bordered k-tridiagonal linear system having n equations and n unknowns. The proposed algorithm is derived by using partition together w...In the current paper, the authors present a symbolic algorithm for solving doubly bordered k-tridiagonal linear system having n equations and n unknowns. The proposed algorithm is derived by using partition together with UL factorization. The cost of the algorithm is O(n). The algorithm is implemented using the computer algebra system, MAPLE. Some illustrative examples are given.展开更多
A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such m...A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods.展开更多
This research aims to plan a “good-enough” schedule with leveling of resource contentions. We use the existing critical chain project management-max-plus linear framework. Critical chain project management is known ...This research aims to plan a “good-enough” schedule with leveling of resource contentions. We use the existing critical chain project management-max-plus linear framework. Critical chain project management is known as a technique used to both shorten the makespan and observe the due date under limited resources;the max-plus linear representation is an approach for modeling discrete event systems as production systems and project scheduling. If a contention arises within a single resource, we must resolve it by appending precedence relations. Thus, the resolution framework is reduced to a combinatorial optimization. If we aim to obtain the exact optimal solution, the maximum computation time is longer than 10 hours for 20 jobs. We thus experiment with Simulated Annealing (SA) and Genetic Algorithm (GA) to obtain an approximate solution within a practical time. Comparing the two methods, the former was beneficial in computation time, whereas the latter was better in terms of the performance of the solution. If the number of tasks is 50, the solution using SA is better than that using GA.展开更多
In this paper, two theorems are proved for zero cost function (or precise I/O mapping) training algorithms about three-layered feedforward neural networks. Two training algorithms based on Moore-Penrose pseudoinverse ...In this paper, two theorems are proved for zero cost function (or precise I/O mapping) training algorithms about three-layered feedforward neural networks. Two training algorithms based on Moore-Penrose pseudoinverse (MPPI) matrix together with corresponding structure design guidelines are also proposed.展开更多
We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the s...We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.展开更多
In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is an...In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.展开更多
Algebraic attack was applied to attack Filter-Combintr model keystreamgenerators. We proposed the technique of function composition to improve the model, and the improvedmodel can resist the algebraic attack. A new cr...Algebraic attack was applied to attack Filter-Combintr model keystreamgenerators. We proposed the technique of function composition to improve the model, and the improvedmodel can resist the algebraic attack. A new criterion for designing Filter-Combiner model was alsoproposed: the total length I. of Linear Finite State Machines used in the model should be largeenough and the degree d of Filter-Combiner function should be approximate [L/2].展开更多
基金This project is supported by National Natural Science Foundation of China (No.59805001)
文摘A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can easily be got by directly solving linear matrixequations rather than structure motion differential equations. Moreover, in order to solve thecorresponding linear matrix equations, the numerical integration fast algorithm is presented. Thenaccording to the results, dynamic design and life-span estimation can be done. Besides, the newalgorithm can solve non-proportion damp structure response.
基金Supported by the National Natural Science Foundation of China (61862033, 61762049, 61902162)Jiangxi Provincial Natural Science Foundation (20202BABL202026, 20202BABL202025, 20202BAB202015)。
文摘The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.
文摘In this paper we proposed an AMH Supply Chain model to obtain optimal solutions for Two-, Three- and Four-Stage for deterministic models. Besides deriving its algebraic solutions, a simple searching method is successfully applied in obtaining optimal total costs and its integer multipliers. Our model has shown promising results in comparison to Equal Cycle Time and other existing ones. The tests focused on obtaining optimal total annual costs and other related details of Two-, Three- and Four-Stage for deterministic models. The results are run under Visual Basic Programming platform using Intel? CoreTM2 Duo T6500 Processor.
基金supported by the National Basic Research Program (973 Program) of China under Grant No.2010CB428804 and 2011CB 309702
文摘The desire to increase spatial and temporal resolution in modeling groundwater system has led to the requirement for intensive computational ability and large memory space. In the course of satisfying such requirement, parallel computing has played a core role over the past several decades. This paper reviews the parallel algebraic linear solution methods and the parallel implementation technologies for groundwater simulation. This work is carried out to provide guidance to enable modelers of groundwater systems to make sensible choices when developing solution methods based upon the current state of knowledge in parallel computing.
文摘In this paper, a parallel simulation algorithm for the control problem in differential algebraic system is presented. The error of the algorithm is estimated. The stability analysis is made for a model problem and the stability region is given. The numerical example demonstrates that the method is efficient.
文摘The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decision diagram (ADD) or variants thereof provides canonical forms to represent and manipulate Boolean functions and pseudo-Boolean functions efficiently. ADD and OBDD-based symbolic algorithms give improved results for large-scale combinatorial optimization problems by searching nodes and edges implicitly. We present novel symbolic ADD formulation and algorithm for maximum weighted matching in bipartite graphs. The symbolic algorithm implements the Hungarian algorithm in the context of ADD and OBDD formulation and manipulations. It begins by setting feasible labelings of nodes and then iterates through a sequence of phases. Each phase is divided into two stages. The first stage is building equality bipartite graphs, and the second one is finding maximum cardinality matching in equality bipartite graph. The second stage iterates through the following steps: greedily searching initial matching, building layered network, backward traversing node-disjoint augmenting paths, updating cardinality matching and building residual network. The symbolic algorithm does not require explicit enumeration of the nodes and edges, and therefore can handle many complex executions in each step. Simulation experiments indicate that symbolic algorithm is competitive with traditional algorithms.
基金Supported by National Natural Science Foundation of China(6980 30 0 7)
文摘How to verify that a given fuzzy set A∈F(X *) is a fuzzy code? In this paper, an algorithm of test has been introduced and studied with the example of test. The measure notion for a fuzzy code and a precise formulation of fuzzy codes and words have been discussed. sification:90K20,94D05.
基金the National Natural Science Foundation of China (No. 19871080)
文摘A class of parallel Rosenbrock methods for differential algebraic equations are presented in this paper. The local truncation errors are defined and the order conditions are established by using the DA-trees and DA-series. The paper also deals with the convergence of the parallel Rosenbrock methods for h -> 0 and states the bounds for the global errors of the methods. Some particular methods are obtained by solving the order equations and a numerical example is given, from which the theoretical orders are actually observed.
文摘It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used successfully to improve the image quality. This paper studies the application of iterative algorithms in radar imaging. A discrete model is first derived, and the iterative algorithms are then adapted to radar imaging. Although such algorithms are usually time consuming, this paper shows that, if the algorithms are appropriately simplified, it is possible to realize them even in real time. The efficiency of iterative algorithms is shown through computer simulations.
文摘Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosenbrock methods are effective. Applying the methods, a fast and high-precision numerical algorithm is given to deal with typical discontinuous parts, which occur frequently in differential-algebraic systems(DAS).
文摘Suppose C is an irreducible algebraic curve of genus g, C*(D,G) is an algebraic geometric code with designed minimum distance d* = deg(G)-2g + 2. In this paper, a decoding algorithm based on Fundamental Iterative Algorithm(FIA) is presented, also its reasonableness is proved. In fact, our decoding algorithm is a modification of the algorithm proposed by G. L. Fend and T. R. N. Rao(1993) and can correct any received words with errors not more than (d*-1)/2, whereas the complexity is only about one half as much as Feng and Rao’s. The procedure can be implemented easily by hardware or software.
文摘In the current paper, the authors present a symbolic algorithm for solving doubly bordered k-tridiagonal linear system having n equations and n unknowns. The proposed algorithm is derived by using partition together with UL factorization. The cost of the algorithm is O(n). The algorithm is implemented using the computer algebra system, MAPLE. Some illustrative examples are given.
文摘A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods.
文摘This research aims to plan a “good-enough” schedule with leveling of resource contentions. We use the existing critical chain project management-max-plus linear framework. Critical chain project management is known as a technique used to both shorten the makespan and observe the due date under limited resources;the max-plus linear representation is an approach for modeling discrete event systems as production systems and project scheduling. If a contention arises within a single resource, we must resolve it by appending precedence relations. Thus, the resolution framework is reduced to a combinatorial optimization. If we aim to obtain the exact optimal solution, the maximum computation time is longer than 10 hours for 20 jobs. We thus experiment with Simulated Annealing (SA) and Genetic Algorithm (GA) to obtain an approximate solution within a practical time. Comparing the two methods, the former was beneficial in computation time, whereas the latter was better in terms of the performance of the solution. If the number of tasks is 50, the solution using SA is better than that using GA.
文摘In this paper, two theorems are proved for zero cost function (or precise I/O mapping) training algorithms about three-layered feedforward neural networks. Two training algorithms based on Moore-Penrose pseudoinverse (MPPI) matrix together with corresponding structure design guidelines are also proposed.
基金Supported by the National Natural Science Foundation of China(11471102,61301229)Supported by the Natural Science Foundation of Henan University of Science and Technology(2014QN039)
文摘We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.
基金Supported by the Natlonal Natural Science Foundation of China
文摘In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.
文摘Algebraic attack was applied to attack Filter-Combintr model keystreamgenerators. We proposed the technique of function composition to improve the model, and the improvedmodel can resist the algebraic attack. A new criterion for designing Filter-Combiner model was alsoproposed: the total length I. of Linear Finite State Machines used in the model should be largeenough and the degree d of Filter-Combiner function should be approximate [L/2].
