In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-m...In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.展开更多
A novel method based on ant colony optimization (ACO), algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from th...A novel method based on ant colony optimization (ACO), algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from the behavior of real ants. ACO algorithm is first introduced, a kind of positive feedback mechanism is adopted in ACO. Then, the solu- tion problem of linear systems of equations was reformulated as an unconstrained optimization problem for solution by an ACID algorithm. Finally, the ACID with other traditional methods is applied to solve a kind of multi-dimensional Hilbert ill-conditioned linear equations. The numerical results demonstrate that ACO is effective, robust and recommendable in solving ill-conditioned linear systems of equations.展开更多
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the‘sender-receiver’model,we propose quantum algorithms for matrix operations such as matrix-ve...Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the‘sender-receiver’model,we propose quantum algorithms for matrix operations such as matrix-vector product,matrix-matrix product,the sum of two matrices,and the calculation of determinant and inverse matrix.We encode the matrix entries into the probability amplitudes of the pure initial states of senders.After applying proper unitary transformation to the complete quantum system,the desired result can be found in certain blocks of the receiver’s density matrix.These quantum protocols can be used as subroutines in other quantum schemes.Furthermore,we present an alternative quantum algorithm for solving linear systems of equations.展开更多
Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations (SSLE) algorithm generating feasible iterates is proposed for solving no...Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations (SSLE) algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.展开更多
Presents information on a study which proposed a superlinearly convergent algorithm of sequential systems of linear equations or nonlinear optimization problems with inequality constraints. Assumptions; Discussion on ...Presents information on a study which proposed a superlinearly convergent algorithm of sequential systems of linear equations or nonlinear optimization problems with inequality constraints. Assumptions; Discussion on lemmas about several matrices related to the common coefficient matrix F; Strengthening of the regularity assumptions on the functions involved; Numerical experiments.展开更多
This paper investigates the distribution of contact resistance of the aluminum alloy in the squeeze stage. A new method of measuring path' s resistance is proposed firstly. Contact resistances are calculated accurate...This paper investigates the distribution of contact resistance of the aluminum alloy in the squeeze stage. A new method of measuring path' s resistance is proposed firstly. Contact resistances are calculated accurately by the systems of 5 linear equations and solutions show that three contact resistances are different. The probability density functions of contact resistance in workpiece/workpiece( W/W) and upper electrode/workpiece( E/W) show that the curve shape has steeper peak and heavier tail than that of the normal distribution. Non-parameter hypothesis test is performed and the result shows that R2 , R4 reject the normal distribution using chi-square and kolmogoroo statistic D method. Therefore, the Asymmetric Laplace distribution is fitted to empirical distributions and is applied to quantify the influence of random contact resistance. The result illustrates that AL distribution is very close to contact resistance of W/W and upper E/W and normal distribution has some deviation. The paper is helpful to research the initial nugget conditions, weldability and the transient multi-coupling field.展开更多
This paper proposes a parallel algorithm, called KDOP (K-DimensionalOptimal Parallel algorithm), to solve a general class of recurrence equations efficiently. The KDOP algorithm partitions the computation into a serie...This paper proposes a parallel algorithm, called KDOP (K-DimensionalOptimal Parallel algorithm), to solve a general class of recurrence equations efficiently. The KDOP algorithm partitions the computation into a series of sub-computations, each of which is executed in the fashion that all the processors work simultaneously with each one executing an optimal sequential algorithm to solve a subcomputation task. The algorithm solves the equations in O(N/p)steps in EREW PRAM model (Exclusive Read Exclusive Write Parallel Ran-dom Access Machine model) using p<N1-e processors, where N is the size of the problem, and e is a given constant. This is an optimal algorithm (itsspeedup is O(p)) in the case of p<N1-e. Such an optimal speedup for this problem was previously achieved only in the case of p<N0.5. The algorithm can be implemented on machines with multiple processing elements or pipelined vector machines with parallel memory systems.展开更多
For the large sparse systems of linear and nonlinear equations, a new class of generalized asynchronous parallel multisplitting iterative method is presented, and its convergence theory is established under suitable c...For the large sparse systems of linear and nonlinear equations, a new class of generalized asynchronous parallel multisplitting iterative method is presented, and its convergence theory is established under suitable conditions. This method not only unifies the discussions of various existing asynchronous multisplitting iterations, but also affords new algorithmic and theoretical results for the parallel solution of large sparse system of linear equations. Besides its generality, this method is also much more suitable for implementing on the MIMD multiprocessor systems.展开更多
文摘In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.
文摘A novel method based on ant colony optimization (ACO), algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from the behavior of real ants. ACO algorithm is first introduced, a kind of positive feedback mechanism is adopted in ACO. Then, the solu- tion problem of linear systems of equations was reformulated as an unconstrained optimization problem for solution by an ACID algorithm. Finally, the ACID with other traditional methods is applied to solve a kind of multi-dimensional Hilbert ill-conditioned linear equations. The numerical results demonstrate that ACO is effective, robust and recommendable in solving ill-conditioned linear systems of equations.
基金supported by the National Natural Science Foundation of China(Grant No.12031004 and Grant No.12271474,61877054)the Fundamental Research Foundation for the Central Universities(Project No.K20210337)+1 种基金the Zhejiang University Global Partnership Fund,188170+194452119/003partially funded by a state task of Russian Fundamental Investigations(State Registration No.FFSG-2024-0002)。
文摘Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the‘sender-receiver’model,we propose quantum algorithms for matrix operations such as matrix-vector product,matrix-matrix product,the sum of two matrices,and the calculation of determinant and inverse matrix.We encode the matrix entries into the probability amplitudes of the pure initial states of senders.After applying proper unitary transformation to the complete quantum system,the desired result can be found in certain blocks of the receiver’s density matrix.These quantum protocols can be used as subroutines in other quantum schemes.Furthermore,we present an alternative quantum algorithm for solving linear systems of equations.
基金Supported by National Natural Science Foundation of China (Grant No. 10771040)Guangxi Science Foundation (Grant No. 0832052)Guangxi University for Nationalities Youth Foundation (Grant No. 2007QN24)
文摘Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations (SSLE) algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.
基金This research was supported by the National Natural Science Foundation of China(19571001, 19971002, 79970014) Cross-century Excellent Personnel Award and Teaching and Research Award Program for Outstanding Young Teachers in High Education Ministry o
文摘Presents information on a study which proposed a superlinearly convergent algorithm of sequential systems of linear equations or nonlinear optimization problems with inequality constraints. Assumptions; Discussion on lemmas about several matrices related to the common coefficient matrix F; Strengthening of the regularity assumptions on the functions involved; Numerical experiments.
基金This research was supported by National Natural Science Foundation of China(No50575159)Project of Chinese Ministry ofEducation(No106049, 20060056058)Natural Science Foundation of Tianjin (06YFJMJC03400)
文摘This paper investigates the distribution of contact resistance of the aluminum alloy in the squeeze stage. A new method of measuring path' s resistance is proposed firstly. Contact resistances are calculated accurately by the systems of 5 linear equations and solutions show that three contact resistances are different. The probability density functions of contact resistance in workpiece/workpiece( W/W) and upper electrode/workpiece( E/W) show that the curve shape has steeper peak and heavier tail than that of the normal distribution. Non-parameter hypothesis test is performed and the result shows that R2 , R4 reject the normal distribution using chi-square and kolmogoroo statistic D method. Therefore, the Asymmetric Laplace distribution is fitted to empirical distributions and is applied to quantify the influence of random contact resistance. The result illustrates that AL distribution is very close to contact resistance of W/W and upper E/W and normal distribution has some deviation. The paper is helpful to research the initial nugget conditions, weldability and the transient multi-coupling field.
文摘This paper proposes a parallel algorithm, called KDOP (K-DimensionalOptimal Parallel algorithm), to solve a general class of recurrence equations efficiently. The KDOP algorithm partitions the computation into a series of sub-computations, each of which is executed in the fashion that all the processors work simultaneously with each one executing an optimal sequential algorithm to solve a subcomputation task. The algorithm solves the equations in O(N/p)steps in EREW PRAM model (Exclusive Read Exclusive Write Parallel Ran-dom Access Machine model) using p<N1-e processors, where N is the size of the problem, and e is a given constant. This is an optimal algorithm (itsspeedup is O(p)) in the case of p<N1-e. Such an optimal speedup for this problem was previously achieved only in the case of p<N0.5. The algorithm can be implemented on machines with multiple processing elements or pipelined vector machines with parallel memory systems.
文摘For the large sparse systems of linear and nonlinear equations, a new class of generalized asynchronous parallel multisplitting iterative method is presented, and its convergence theory is established under suitable conditions. This method not only unifies the discussions of various existing asynchronous multisplitting iterations, but also affords new algorithmic and theoretical results for the parallel solution of large sparse system of linear equations. Besides its generality, this method is also much more suitable for implementing on the MIMD multiprocessor systems.