Two New FCT Algorithms Based on Product System

In this paper we present a product system and give a representation for consine functions with the system. Based on the formula two new algorithms are designed for computing the Discrete Cosine Transform. Both algorithms have regular recursive structure and good numerical stability and are easy to parallize.     

微分代数问题的一类数值算法

其中y和f的维数为l,u和g的维数为m.假定函数f和g具有如下要求的连续导数且矩阵g_y(y)f_u(t,y,u)具有有界逆矩阵,即存在M>0,使‖(g_y(y)f_u(t,y,u))~(-1)‖≤M.     

Some inversion algorithms for discrete systems

Several algorithms are proposed to solve the inversion problem in the presence of information about the system state or the system output under certain additional assumptions (the wave model of the unknown input is assumed known). The problem of estimation from the output is solved by constructing state observers for a system of arbitrary relative order. Necessary conditions for the applicability of the proposed algorithms are identified. Error bounds of the approximation algorithms are estimated. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 119–126, 2004.     

Positional robust inversion in nonlinear dynamical systems

The article studies robust inversion of nonlinear dynamical systems using a known phase vector. Inversion algorithms are proposed for the case when the system dynamics is exactly known. These algorithms solve the inversion problem with any prespecified accuracy. Algorithms solving the inversion problem with perturbed system dynamics are also considered. Accuracy bounds are obtained for the various algorithms. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 3, pp. 5–18, 2003.     

On the Complexity of Exclusion Algorithms for Optimization

Exclusion algorithms are a well-known tool in the area of interval analysis for finding all solutions of a system of nonlinear equations or for finding the global minimum of a function over a compact domain. The present paper discusses a new class of tests for such algorithms in the context of global optimization and presents complexity results concerning the resulting algorithms.     

A robustness approach to uncapacitated network design problems

In this paper, we address uncapacitated network design problems characterised by uncertainty in the input data. Network design choices have a determinant impact on the effectiveness of the system. Design decisions are frequently made with a great degree of uncertainty about the conditions under which the system will be required to operate. Instead of finding optimal designs for a given future scenario, designers often search for network configurations that are “good” for a variety of likely future scenarios. This approach is referred to as the “robustness” approach to system design. We present a formal definition of “robustness” for the uncapacitated network design problem, and develop algorithms aimed at finding robust network designs. These algorithms are adaptations of the Benders decomposition methodology that are tailored so they can efficiently identify robust network designs. We tested the proposed algorithms on a set of randomly generated problems. Our computational experiments showed two important properties. First, robust solutions are abundant in uncapacitated network design problems, and second, the proposed algorithms performance is satisfactory in terms of cost and number of robust network designs obtained.     

Algorithms for solving inverse geophysical problems on parallel computing systems

For solving inverse gravimetry problems, efficient stable parallel algorithms based on iterative gradient methods are proposed. For solving systems of linear algebraic equations with block-tridiagonal matrices arising in geoelectrics problems, a parallel matrix sweep algorithm, a square root method, and a conjugate gradient method with preconditioner are proposed. The algorithms are implemented numerically on a parallel computing system of the Institute of Mathematics and Mechanics (PCS-IMM), NVIDIA graphics processors, and an Intel multi-core CPU with some new computing technologies. The parallel algorithms are incorporated into a system of remote computations entitled “Specialized Web-Portal for Solving Geophysical Problems on Multiprocessor Computers.” Some problems with “quasi-model” and real data are solved.     

Algorithms of filtration and extrapolation for discrete-time dynamical systems

The bases of theory and the recursive filtration algorithms ensuring the guaranteed precision of estimate for an extrapolated state of a dynamic system are described. A determined precision is ensured by corresponding choice of algorithm parameters.The different algorithms of filtration and extrapolation are investigated. These algorithms may be used in constructing tracking systems, organizing of corresponding measurements and estimation of parameters in information systems.     

Primal-Dual Path-Following Algorithms for Determinant Maximization Problems With Linear Matrix Inequalities

Primal-dual path-following algorithms are considered for determinant maximization problem (maxdet-problem). These algorithms apply Newton's method to a primal-dual central path equation similar to that in semidefinite programming (SDP) to obtain a Newton system which is then symmetrized to avoid nonsymmetric search direction. Computational aspects of the algorithms are discussed, including Mehrotra-type predictor-corrector variants. Focusing on three different symmetrizations, which leads to what are known as the AHO, H..K..M and NT directions in SDP, numerical results for various classes of maxdet-problem are given. The computational results show that the proposed algorithms are efficient, robust and accurate.     

A variable dimension solution approach for the general spatial price equilibrium problem

Algorithms are presented that are specifically designed for solving general nonlinear multicommodity spatial price equilibrium problems, i.e., problems with nonlinear transportation cost functions, nonlinear supply and demand functions, inter-commodity congestion effects, intercommodity substitution and complementarity effects and interactions among transportation links and among spatially separated markets. The algorithms are specializations of an iterative method for solving nonlinear complementarity problems that requires solving a system of nonlinear equations at each iteration. The algorithms exploit the network structure of the problems to reduce the size of the system of equations to be solved at each iteration. The decision rules for determining which equations are to be included in the system at each iteration are extremely simple, and the remainder of the computational work is carried out by the nonlinear equation solver. Because of this, the algorithms are very easy to implement with readily available software. In addition, since the decision rules only require sign information, only the final system needs to be solved with precision.     

A numerical analysis of two point boundary value problem algorithms

The mathematical modeling of optimal control system problems is a method applied in industry to obtain correct electrical and mechanical design parameters once the system equations have been derived. The algorithms required to implement the control loop for these applications must provide stable, relatively accurate, efficient solutions.The purpose of this paper is to address the computational characteristics which would concern a system designer in the consideration of the selection of an effective algorithm to implement a two-point boundary value problem solution. Three Invariant Imbedding Algorithms are evaluated for a worst case and a best case problem by an adaptation of four methods of analysis. The areas of computer science, numerical analysis and Turing Machine Theory are drawn upon in these methods to implement and compare the computational form of the algorithms. The four analysis techniques indicated consistent results for the three two-point boundary value problem algorithms considered. Applications of two-point boundary value problem algorithms occur in problems of nuclear reactor heat transfer, pollution control, fluidics, vibration and magnetics.     

Convergence of Non-stationary Parallel Multisplitting Methods for Hermitian Positive Definite Matrices

Non-stationary multisplitting algorithms for the solution of linear systems are studied. Convergence of these algorithms is analyzed when the coefficient matrix of the linear system is hermitian positive definite. Asynchronous versions of these algorithms are considered and their convergence investigated.

     

On the preconditioning of the block tridiagonal linear system of equations

Two algorithms for computing the inverse factors of general tridiagonal and pentadiagonal matrices are obtained. Then, these algorithms are used for computing a block ILU preconditioner for the block tridiagonal linear system of equations. Some numerical results are given to show the robustness and efficiency of the preconditioner. The performance of the proposed preconditioner is compared with a recently proposed method.     

RECURSIVE SYSTEM IDENTIFICATION

Most of existing methods in system identification with possible exception of those for linear systems are off-line in nature, and hence are nonrecursive. This paper demonstrates the recent progress in recursive system identification. The recursive identification algorithms are presented not only for linear systems （multivariate ARMAX systems） but also for nonlinear systems such as the Hammerstein and Wiener systems, and the nonlinear ARX systems. The estimates generated by the algorithms are online updated and converge a.s. to the true values as time tends to infinity.     

Algorithms for solving nonlinear dynamic decision models

In this paper we discuss two Newton-type algorithms for solving economic models. The models are preprocessed by reordering the equations in order to minimize the dimension of the simultaneous block. The solution algorithms are then applied to this block. The algorithms evaluate numerically, as required, selected columns of the Jacobian of the simultaneous part. Provisions also exist for similar systems to be solved, if possible, without actually reinitialising the Jacobian. One of the algorithms also uses the Broyden update to improve the Jacobian. Global convergence is maintained by an Armijo-type stepsize strategy.The global and local convergence of the quasi-Newton algorithm is discussed. A novel result is established for convergence under relaxed descent directions and relating the achievement of unit stepsizes to the accuracy of the Jacobian approximation. Furthermore, a simple derivation of the Dennis-Moré characterisation of the Q-superlinear convergence rate is given.The model equation reordering algorithm is also described. The model is reordered to define heart and loop variables. This is also applied recursively to the subgraph formed by the loop variables to reduce the total number of above diagonal elements in the Jacobian of the complete system. The extension of the solution algorithms to consistent expectations are discussed. The algorithms are compared with Gauss-Seidel SOR algorithms using the USA and Spanish models of the OECD Interlink system.     

A cell exclusion algorithm for determining all the solutions of a nonlinear system of equations

A new group of methods named cell exclusion algorithms (CEAs) is developed for finding all the solutions of a nonlinear system of equations. These types of algorithms, different in principle from those of homotopy, interval and cell-mapping-dynamical-analysis approaches, are based on cellular discretization and the use of a certain simple necessity test of the solutions. The main advantages of the algorithms are their simplicity, reliability, and general applicability. Having all features of interval techniques (but without using interval arithmetic) and with complexity O(log(1/)), the algorithms improve significantly on both the interval algorithms and the cell mapping techniques. Theoretical analysis and numerical simulations both demonstrate that CEAs are very efficient.     

Modeling and optimizing a vendor managed replenishment system using machine learning and genetic algorithms

Using a supply chain network, we demonstrate the feasibility, viability, and robustness of applying machine learning and genetic algorithms to respectively model, understand, and optimize such data intensive environments. Deployment of these algorithms, which learn from and optimize data, can obviate the need to perform more complex, expensive, and time consuming design of experiments (DOE), which usually disrupt system operations. We apply and compare the behavior and performance of the proposed machine learning algorithms to that obtained via DOE in a simulated Vendor Managed Replenishment system, developed for an actual firm. The results show that the models resulting from the proposed algorithms had strong explanatory and predictive power, comparable to that of DOE. The optimal system settings and profit were also similar to that obtained from DOE. The virtues of using machine learning and evolutionary algorithms to model and optimize data rich environments thus seem promising because they are automatic, involving little human intervention and expertise. We believe and are exploring how they can be made adaptive to improve parameter estimates with increasing data, as well as seamlessly detecting system (and therefore model) changes, thus being capable of recursively updating and reoptimizing a modified or new model.     

Convergence analysis of nonmonotone Levenberg-Marquardt algorithms for complementarity problem

This paper addresses the convergence of two nonmonotone Levenberg-Marquardt algorithms for nonlinear complementarity problem. Under some mild assumptions, and requiring only the solution of a linear system at each iteration, the nonmonotone Levenberg-Marquardt algorithms are shown to be globally convergent.     

On splitting schemes in the mixed finite element method

Within the research into some geothermal modes, a 3D heat transfer process was described by a first-order system of differential equations (in terms of “temperature-heat-flow”). This system was solved by an explicit scheme for the mixed finite element spatial approximations based on the Raviart-Thomas degrees of freedom. In this paper, several algorithms based on the splitting technique for the vector heat-flow equation are proposed. Some comparison results of accuracy of the algorithms proposed are presented.