19 results
Search Results
2. INERTIAL-TYPE PROJECTION METHODS FOR SOLVING CONVEX CONSTRAINED MONOTONE NONLINEAR EQUATIONS WITH APPLICATIONS TO ROBOTIC MOTION CONTROL.
- Author
-
MUHAMMAD, ABUBAKAR BAKOJI, TAMMER, CHRISTIANE, AWWAL, ALIYU MUHAMMED, ELSTER, ROSALIND, and ZHAOLI MA
- Subjects
ITERATIVE methods (Mathematics) ,NONLINEAR analysis ,STOCHASTIC convergence ,NUMERICAL analysis ,ALGORITHMS - Abstract
In this paper, we introduce two derivative-free projection iterative algorithms for solving a system of nonlinear monotone operator equations. The two proposed algorithms can be viewed as twostep methods where the first step uses an inertial effect in every iteration. The global convergence of the proposed algorithms is established under some mild assumptions. We present numerical experiments to show the efficiency and advantage of the inertial projection steps of the proposed algorithms and compare it with some existing methods for solving nonlinear problems. Finally, we consider the problem of solving a motion control problem involving a two-joint planar robotic manipulator. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
3. Numerical Implementation of the Fictitious Domain Method for Elliptic Equations.
- Author
-
Temirbekov, Almas N. and Wójcik, Waldemar
- Subjects
ELLIPTIC equations ,COEFFICIENTS (Statistics) ,ITERATIVE methods (Mathematics) ,STOCHASTIC convergence ,ALGORITHMS ,COMPUTATIONAL complexity ,NUMERICAL analysis ,DIRICHLET problem - Abstract
In this paper, we consider an elliptic equation with strongly varying coefficients. Interest in the study of these equations is connected with the fact that this type of equation is obtained when using the fictitious domain method. In this paper, we propose a special method for the numerical solution of elliptic equations with strongly varying coefficients. A theorem is proved for the rate of convergence of the iterative process developed. A computational algorithm and numerical calculations are developed to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
4. Copula-Based Approach to Synthetic Population Generation.
- Author
-
Jeong, Byungduk, Lee, Wonjoon, Kim, Deok-Soo, and Shin, Hayong
- Subjects
SIMULATION methods & models ,TRANSPORTATION planning ,ITERATIVE methods (Mathematics) ,DEPENDENCE (Statistics) ,APPLIED mathematics - Abstract
Generating synthetic baseline populations is a fundamental step of agent-based modeling and simulation, which is growing fast in a wide range of socio-economic areas including transportation planning research. Traditionally, in many commercial and non-commercial microsimulation systems, the iterative proportional fitting (IPF) procedure has been used for creating the joint distribution of individuals when combining a reference joint distribution with target marginal distributions. Although IPF is simple, computationally efficient, and rigorously founded, it is unclear whether IPF well preserves the dependence structure of the reference joint table sufficiently when fitting it to target margins. In this paper, a novel method is proposed based on the copula concept in order to provide an alternative approach to the problem that IPF resolves. The dependency characteristic measures were computed and the results from the proposed method and IPF were compared. In most test cases, the proposed method outperformed IPF in preserving the dependence structure of the reference joint distribution. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
5. Efficient Hardware Design of Iterative Stencil Loops.
- Author
-
Rana, Vincenzo, Beretta, Ivan, Bruschi, Francesco, Nacci, Alessandro A., Atienza, David, and Sciuto, Donatella
- Subjects
ALGORITHMS ,ITERATIVE methods (Mathematics) ,NUMERICAL analysis ,ALGEBRA ,MAGNITUDE (Mathematics) - Abstract
A large number of algorithms for multidimensional signals processing and scientific computation come in the form of iterative stencil loops (ISLs), whose data dependencies span across multiple iterations. Because of their complex inner structure, automatic hardware acceleration of such algorithms is traditionally considered as a difficult task. In this paper, we introduce an automatic design flow that identifies, in a wide family of bidimensional data processing algorithms, subportions that exhibit a kind of parallelism close to that of ISLs; these are mapped onto a space of highly optimized ad-hoc architectures, which is efficiently explored to identify the best implementations with respect to both area and throughput. Experimental results show that the proposed methodology generates circuits whose performance is comparable to that of manually optimized solutions, and orders of magnitude higher than those generated by commercial high-level synthesis tools. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
6. A new iterative scheme for numerical reckoning fixed points of total asymptotically nonexpansive mappings.
- Author
-
Pansuwan, Adoon and Sintunavarat, Wutiphol
- Subjects
NONEXPANSIVE mappings ,NUMERICAL analysis ,ITERATIVE methods (Mathematics) ,ALGORITHMS ,ECONOMIC convergence - Abstract
In this paper, we propose a new iterative algorithm to approximate fixed points of total asymptotically nonexpansive mappings in $\operatorname{CAT}(0)$ spaces. We also provide two examples to illustrate the convergence behavior of the proposed algorithm and numerically compare the convergence of the proposed iteration scheme with the existing schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
7. A Landmark-Free Method for Three-Dimensional Shape Analysis.
- Author
-
Pomidor, Benjamin J., Makedonska, Jana, and Slice, Dennis E.
- Subjects
MORPHOMETRICS ,NUMERICAL analysis ,DATA transformations (Statistics) ,SCANNING systems ,ITERATIVE methods (Mathematics) - Abstract
Background: The tools and techniques used in morphometrics have always aimed to transform the physical shape of an object into a concise set of numerical data for mathematical analysis. The advent of landmark-based morphometrics opened new avenues of research, but these methods are not without drawbacks. The time investment required of trained individuals to accurately landmark a data set is significant, and the reliance on readily-identifiable physical features can hamper research efforts. This is especially true of those investigating smooth or featureless surfaces. Methods: In this paper, we present a new method to perform this transformation for data obtained from high-resolution scanning technology. This method uses surface scans, instead of landmarks, to calculate a shape difference metric analogous to Procrustes distance and perform superimposition. This is accomplished by building upon and extending the Iterative Closest Point algorithm. We also explore some new ways this data can be used; for example, we can calculate an averaged surface directly and visualize point-wise shape information over this surface. Finally, we briefly demonstrate this method on a set of primate skulls and compare the results of the new methodology with traditional geometric morphometric analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
8. Gradient-based iterative algorithms for generalized coupled Sylvester-conjugate matrix equations.
- Author
-
Huang, Bao-Hua and Ma, Chang-Feng
- Subjects
- *
CONJUGATE gradient methods , *ITERATIVE methods (Mathematics) , *NUMERICAL analysis , *ALGORITHMS , *MATRICES (Mathematics) - Abstract
By applying the hierarchical identification principle, the gradient-based iterative algorithm is suggested to solve a class of complex matrix equations. With the real representation of a complex matrix as a tool, the sufficient and necessary conditions for the convergence factor are determined to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Also, we solve the problem which is proposed by Wu et al. (2010). Finally, some numerical examples are provided to illustrate the effectiveness of the proposed algorithms and testify the conclusions suggested in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
9. Locating design point in structural reliability analysis by introduction of a control parameter and moving limited regions.
- Author
-
Shayanfar, Mohsen Ali, Barkhordari, Mohammad Ali, and Roudak, Mohammad Amin
- Subjects
- *
ALGORITHMS , *ACCURACY , *RELIABILITY in engineering , *ITERATIVE methods (Mathematics) , *NUMERICAL analysis - Abstract
In reliability analysis, computation of reliability index and finding design point is still a challenge. In this paper a new efficient reliability algorithm to locate design point is proposed. The proposed algorithm takes benefit from two significant means in its efficient search for the design point. One means is an updating rule by which the candidate of design point is updated and moved towards real design point. The criteria of updating in this rule are designed such that the candidate moves on an effective general path towards real design point. The other means is the introduction of a control parameter by which the search process at each iteration is limited to a relatively small region. This parameter controls the candidate of design point on its defined general path and does not let it leave the path. These two means have made the proposed algorithm very reliable in finding design point. Through numerical examples the accuracy and efficiency of the proposed algorithm is shown. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
10. COMMON SOLUTIONS TO PSEUDOMONOTONE EQUILIBRIUM PROBLEMS.
- Author
-
HIEU, D. V.
- Subjects
- *
ITERATIVE methods (Mathematics) , *VARIATIONAL inequalities (Mathematics) , *EQUILIBRIUM , *ALGORITHMS , *NUMERICAL analysis - Abstract
In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradientcutting algorithm which is extended from the previously known one for variational inequalities to equilibrium problems. The second is a new cyclic hybrid extragradient-cutting algorithm. In the cyclic algorithm, using the known techniques, we can perform and develop practical numerical experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2016
11. An improved generalized conjugate residual squared algorithm suitable for distributed parallel computing.
- Author
-
Zuo, Xian-Yu, Zhang, Li-Tao, and Gu, Tong-Xiang
- Subjects
- *
DISTRIBUTED computing , *GENERALIZATION , *ALGORITHMS , *NUMERICAL analysis , *PARALLEL computers , *ITERATIVE methods (Mathematics) - Abstract
Abstract: In this paper, based on GCRS algorithm in Zhang and Zhao (2010) and the ideas in Gu et al. (2007), we present an improved generalized conjugate residual squared (IGCRS) algorithm that is designed for distributed parallel environments. The new improved algorithm reduces two global synchronization points to one by changing the computation sequence in the GCRS algorithm in such a way that all inner products per iteration are independent so that communication time required for inner products can be overlapped with useful computation. Theoretical analysis and numerical comparison of isoefficiency analysis show that the IGCRS method has better parallelism and scalability than the GCRS method, and the parallel performance can be improved by a factor of about 2. Finally, some numerical experiments clearly show that the IGCRS method can achieve better parallel performance with a higher scalability than the GCRS method and the improvement percentage of communication is up to 52.19% averagely, which meets our theoretical analysis. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
12. Two-level defect-correction Oseen iterative stabilized finite element method for the stationary conduction–convection equations.
- Author
-
Haiyan Su, Jianping Zhao, Dongwei Gui, and Xinlong Feng
- Subjects
- *
FINITE element method , *ITERATIVE methods (Mathematics) , *CONVECTIVE flow , *STOCHASTIC convergence , *ALGORITHMS , *NUMERICAL analysis - Abstract
In this paper, a two-level defect-correction Oseen iterative finite element method is presented for the stationary conduction–convection equations based on local Gauss integration. The method combines the defect-correction method, the two-level strategy, and the locally stabilized method. The stability and convergence of the proposed method are deduced. Finally, numerical examples verify the theoretical results of the proposed algorithm and show that it is highly efficient and reliable for the considered problem. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
13. A Single-Phase, Proximal Path-Following Framework.
- Author
-
Tran-Dinh, Quoc, Kyrillidis, Anastasios, and Cevher, Volkan
- Subjects
SMOOTHNESS of functions ,NONLINEAR analysis ,ITERATIVE methods (Mathematics) ,NUMERICAL analysis ,ALGORITHMS - Abstract
We propose a new proximal path-following framework for a class of constrained convex problems. We consider settings where the nonlinear—and possibly nonsmooth—objective part is endowed with a proximity operator, and the constraint set is equipped with a self-concordant barrier. Our approach relies on the following two main ideas. First, we reparameterize the optimality condition as an auxiliary problem, such that a good initial point is available; by doing so, a family of alternative paths toward the optimum is generated. Second, we combine the proximal operator with path-following ideas to design a single-phase, proximal path-following algorithm. We prove that our algorithm has the same worst-case iteration complexity bounds as in standard path-following methods from the literature but does not require an initial phase. Our framework also allows inexactness in the evaluation of proximal Newton directions, without sacrificing the worst-case iteration complexity. We demonstrate the merits of our algorithm via three numerical examples, where proximal operators play a key role. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
14. Single image super-resolution based on approximated Heaviside functions and iterative refinement.
- Author
-
Wang, Xin-Yu, Huang, Ting-Zhu, and Deng, Liang-Jian
- Subjects
HIGH resolution imaging ,DISCONTINUOUS functions ,ITERATIVE methods (Mathematics) ,MATHEMATICAL regularization ,IMAGE analysis - Abstract
One method of solving the single-image super-resolution problem is to use Heaviside functions. This has been done previously by making a binary classification of image components as “smooth” and “non-smooth”, describing these with approximated Heaviside functions (AHFs), and iteration including l
1 regularization. We now introduce a new method in which the binary classification of image components is extended to different degrees of smoothness and non-smoothness, these components being represented by various classes of AHFs. Taking into account the sparsity of the non-smooth components, their coefficients are l1 regularized. In addition, to pick up more image details, the new method uses an iterative refinement for the residuals between the original low-resolution input and the downsampled resulting image. Experimental results showed that the new method is superior to the original AHF method and to four other published methods. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
15. An Improved DINEOF Algorithm for Filling Missing Values in Spatio-Temporal Sea Surface Temperature Data.
- Author
-
Ping, Bo, Su, Fenzhen, and Meng, Yunshan
- Subjects
OCEAN temperature ,MISSING data (Statistics) ,ITERATIVE methods (Mathematics) ,STOCHASTIC convergence ,IMAGE reconstruction - Abstract
In this study, an improved Data INterpolating Empirical Orthogonal Functions (DINEOF) algorithm for determination of missing values in a spatio-temporal dataset is presented. Compared with the ordinary DINEOF algorithm, the iterative reconstruction procedure until convergence based on every fixed EOF to determine the optimal EOF mode is not necessary and the convergence criterion is only reached once in the improved DINEOF algorithm. Moreover, in the ordinary DINEOF algorithm, after optimal EOF mode determination, the initial matrix with missing data will be iteratively reconstructed based on the optimal EOF mode until the reconstruction is convergent. However, the optimal EOF mode may be not the best EOF for some reconstructed matrices generated in the intermediate steps. Hence, instead of using asingle EOF to fill in the missing data, in the improved algorithm, the optimal EOFs for reconstruction are variable (because the optimal EOFs are variable, the improved algorithm is called VE-DINEOF algorithm in this study). To validate the accuracy of the VE-DINEOF algorithm, a sea surface temperature (SST) data set is reconstructed by using the DINEOF, I-DINEOF (proposed in 2015) and VE-DINEOF algorithms. Four parameters (Pearson correlation coefficient, signal-to-noise ratio, root-mean-square error, and mean absolute difference) are used as a measure of reconstructed accuracy. Compared with the DINEOF and I-DINEOF algorithms, the VE-DINEOF algorithm can significantly enhance the accuracy of reconstruction and shorten the computational time. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
16. Numerical identification of a sparse Robin coefficient.
- Author
-
Sun, Zhiyuan, Jiao, Yuling, Lu, Xiliang, and Jin, Bangti
- Subjects
SEMISMOOTH Newton methods ,NUMERICAL analysis ,INVERSE problems ,ITERATIVE methods (Mathematics) ,LAPLACE distribution ,ALGORITHMS - Abstract
We investigate an inverse problem of identifying a Robin coefficient with a sparse structure in the Laplace equation from noisy boundary measurements. The sparse structure of the Robin coefficient γ is understood as a small perturbation of a reference profile γ in the sense that their difference γ− γ has a small support. This problem is formulated as an optimal control problem with an L-regularization term. An iteratively reweighted least-squares algorithm with an inner semismooth Newton iteration is employed to solve the resulting optimization problem, and the convergence of the iteratively weighted least-squares algorithm is established. Numerical results for two-dimensional problems are presented to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
17. Benson type algorithms for linear vector optimization and applications.
- Author
-
Hamel, Andreas, Löhne, Andreas, and Rudloff, Birgit
- Subjects
APPROXIMATION algorithms ,MATHEMATICAL optimization ,PROBLEM solving ,LINEAR programming ,ITERATIVE methods (Mathematics) ,NUMERICAL analysis - Abstract
New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous versions. Extensions are given to problems with arbitrary pointed solid polyhedral ordering cones. Numerical examples are provided, one of them involving a new set-valued risk measure for multivariate positions. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
18. Robust Distributed Average Consensus via Exchange of Running Sums.
- Author
-
Hadjicostis, Christoforos N., Vaidya, Nitin H., and Dominguez-Garcia, Alejandro D.
- Subjects
MARKOV processes ,ALGORITHMS ,DIRECTED graphs ,ITERATIVE methods (Mathematics) ,NUMERICAL analysis - Abstract
We consider a multi-component system in which each component (node) can send/receive information to/from sets of neighboring nodes via communication links (edges) that form a fixed strongly connected, possibly directed, communication topology (digraph). We analyze a class of distributed iterative algorithms that allow the nodes to asymptotically compute the exact average of their initial values, despite a variety of challenging scenarios, including possible packet drops in the communication links, and imprecise knowledge of the network. The algorithms in this class run the two linear iterations of the so-called ratio-consensus algorithm, modified so that messages sent by one node to another are encoded as running sums. This “convolutional” encoding allows the receiving node $l$ to infer information about past messages that node $j$ meant to send to node $l$ but may have been lost due to packet drops. Imprecise knowledge of the network (unknown out-neighborhoods) can be handled, at the cost of memory and communication overhead, by also having each node track the progress of running sums of other nodes, and forward to its out-neighboring nodes the updated value of one such running sum that it randomly selects. Our analysis relies on augmenting the digraph that describes the communication topology by introducing additional (virtual) nodes, and showing that the dynamics of each of the two iterations in the augmented digraph is mathematically equivalent to a finite inhomogeneous Markov chain. Almost sure convergence to exact average consensus is then established via weak ergodicity analysis of the resulting inhomogeneous Markov chain. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
19. Integrated Hybrid Second Order Algorithm for Orthogonal Projection onto a Planar Implicit Curve.
- Author
-
Li, Xiaowu, Pan, Feng, Cheng, Taixia, Wu, Zhinan, Liang, Juan, and Hou, Linke
- Subjects
ALGORITHMS ,NUMERICAL analysis ,GEOMETRY ,MATHEMATICAL models ,ITERATIVE methods (Mathematics) - Abstract
The computation of the minimum distance between a point and a planar implicit curve is a very important problem in geometric modeling and graphics. An integrated hybrid second order algorithm to facilitate the computation is presented. The proofs indicate that the convergence of the algorithm is independent of the initial value and demonstrate that its convergence order is up to two. Some numerical examples further confirm that the algorithm is more robust and efficient than the existing methods. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.