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On the Robustness of ILU Smoothing 关于ILU平滑的鲁棒性
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910043
G. Wittum
{"title":"On the Robustness of ILU Smoothing","authors":"G. Wittum","doi":"10.1137/0910043","DOIUrl":"https://doi.org/10.1137/0910043","url":null,"abstract":"In the present paper, a detailed analysis of a multigrid method with an ILU smoother applied to a singularly perturbed problem is given. Based on the analysis of a simple anisotropic model problem, a variant of the usual incomplete LU factorization is introduced, which is especially suited as robust smoother. For this variant a detailed analysis and a proof of robustness is given. Furthermore, some contradictions between the smoothing rates predicted by local Fourier analysis and the practically observed convergence factors are explained (see [W. Hackbusch, Multi-grid Methods and Applications, Springer-Verlag, Berlin, Heidelberg, 1985; R. Kettler, “Analysis and comparison of relaxation schemes in robust multi-grid and preconditioned conjugate gradient methods,” in Multi-grid Methods, Lecture Notes in Math. 960, Springer-Verlag, Berlin, 1982; C. A. Thole, Beitrage zur Fourieranalyse von Mehrgitterver fahren, Diplomarbeit, Universitat Bonn, 1983]. The theoretical results are confirmed by numerical tests.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116366122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 175
Waveform iteration and the shifted picard splitting 波形迭代和移位皮卡分裂
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910046
R. Skeel
{"title":"Waveform iteration and the shifted picard splitting","authors":"R. Skeel","doi":"10.1137/0910046","DOIUrl":"https://doi.org/10.1137/0910046","url":null,"abstract":"The theme of this paper is that the primary computational bottleneck in the solution of stiff ordinary differential equations (ODEs) and the parallel solution of nonstiff ODEs is the implicitness of the ODE rather than the approximation of the integration process (or in conventional terminology, numerical stability rather than accuracy), and therefore it may be fruitful to apply (at least conceptually) the iterative techniques needed to overcome implicitness in continuous time, before discretization—to waveforms rather than values at a point in time. Several classical iterations, based on splitting, are discussed, but the emphasis is on those not based on a partitioning of the ODE system. The shifted Picard iteration is proposed as a compromise between the cheap but slow Picard iteration and the fast but expensive Newton iteration. By varying the shift parameter from one iteration to the next, a good rate of convergence seems possible. As an alternative, the author also examines the more classical acceleration technique applied to the Picard iteration. Some experimental results are given. However, the practical aspects of discretization are beyond the scope of this paper.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127452344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 40
An Optimal Complexity Algorithm for Computing the Topological Degree in Two Dimensions 二维拓扑度计算的最优复杂度算法
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910042
T. Boult, K. Sikorski
{"title":"An Optimal Complexity Algorithm for Computing the Topological Degree in Two Dimensions","authors":"T. Boult, K. Sikorski","doi":"10.1137/0910042","DOIUrl":"https://doi.org/10.1137/0910042","url":null,"abstract":"An algorithm is presented for computing the topological degree for any function from a class F. The class F consists of functions $f:C to mathbb{R}^2 $ defined on C, the unit square, which satisfy the Lipschitz condition with constant $K > 0$, and whose infinity norm on the boundary of C is at least $d > 0$. For functions in this class, the algorithm could be useful in solving nonlinear systems of equations and also in other aspects of nonlinear analysis.A worst-case lower bound, $m^ * = 4lfloor {K / {4d}} rfloor $, is established on the number of function evaluations necessary to compute the topological degree for any function f from the class F. The parallel information used by our algorithm permits the computation of the degree for every f in F with $m^ * $ function evaluations. The cost of our algorithm is shown to be almost equal to the complexity of the problem.The algorithm has been implemented and tested. Performance information for a set of 10 systems of equations is reported.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127169232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
The Reduced Basis Method for Incompressible Viscous Flow Calculations 不可压缩粘性流计算的降基法
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910047
J. Peterson
{"title":"The Reduced Basis Method for Incompressible Viscous Flow Calculations","authors":"J. Peterson","doi":"10.1137/0910047","DOIUrl":"https://doi.org/10.1137/0910047","url":null,"abstract":"The reduced basis method is a type of reduction method that can be used to solve large systems of nonlinear equations involving a parameter. In this work, the method is used in conjunction with a standard continuation technique to approximate the solution curve for the nonlinear equations resulting from discretizing the Navier–Stokes equations by finite–element methods. This paper demonstrates that the reduced basis method can be implemented to approximate efficiently solutions to incompressible viscous flows. Choices of basis vectors, issues concerning the implementation of the method, and numerical calculations are discussed. Two fluid flow calculations are considered, the driven cavity problem and flow over a forward facing step.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116632296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 230
Nonstandard scaling matrices for trust region Gauss-Newton methods 信赖域高斯-牛顿方法的非标准标度矩阵
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910040
H. Schwetlick, V. Tiller
{"title":"Nonstandard scaling matrices for trust region Gauss-Newton methods","authors":"H. Schwetlick, V. Tiller","doi":"10.1137/0910040","DOIUrl":"https://doi.org/10.1137/0910040","url":null,"abstract":"For solving large nonlinear least-squares problems via trust region Gauss–Newton methods, nonstandard scaling matrices are proposed for scaling the norm of the step. The scaling matrices are rectangular, of full rank, and contain a block of the Jacobian matrix of the residual function.Three types of such matrices are investigated. The corresponding trust region methods are shown to have qualitatively the same convergence properties as the standard method. Nonstandard scaling matrices are especially intended for solving large and structured problems such as orthogonal distance regression or surface fitting. Initial computational experience suggests that for such problems the proposed scaling implies sometimes a modest increase in the number of iterations but reduces the overall computational costs.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123606819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Computational Behavior of Gauss–Newton Methods 高斯-牛顿方法的计算行为
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910033
C. Fraley
{"title":"Computational Behavior of Gauss–Newton Methods","authors":"C. Fraley","doi":"10.1137/0910033","DOIUrl":"https://doi.org/10.1137/0910033","url":null,"abstract":"This paper is concerned with the numerical behavior of Gauss–Newton methods for nonlinear least-squares problems. It is well known that Gauss–Newton methods often cannot be applied successfully without modification. However, no a priori characterization has been given of those problems on which a particular Gauss–Newton method or class of Gauss–Newton methods will or will not work well. The present paper gives some insight into why it is difficult to do so.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129322978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
A Fast Algorithm for the Numerical Evaluation of Conformal Mappings 保角映射数值求值的快速算法
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910031
S. O'Donnell, V. Rokhlin
{"title":"A Fast Algorithm for the Numerical Evaluation of Conformal Mappings","authors":"S. O'Donnell, V. Rokhlin","doi":"10.1137/0910031","DOIUrl":"https://doi.org/10.1137/0910031","url":null,"abstract":"An algorithm is presented for the construction of conformal mappings from arbitrary simply connected regions in the complex plane onto the unit disk. The algorithm is based on a combination of the Kerzman–Stein integral equation (see [Math. Anal, 236 (1978), pp. 85–93]) and the Fast Multipole Method for the evaluation of Cauchy-type integrals (see [V. Rokhlin, J. Comput. Phys., 60 (1985), pp. 187–207], [L. Greengard and V. Rokhlin, J. Comput. Phys., 73 (1987), pp. 325–348], [J. Carrier, L. Greengard, and V. Rokhlin, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 669–686], [L. F. Greengard, Ph.D. thesis, Department of Computer Science, Yale University, New Haven, CT, 1987]). Previously published methods for the construction of conformal mappings via the Kerzman–Stein equation have an asymptotic CPU time estimate of the order $O(n^2 )$, where n is the number of nodes in the discretization of the boundary of the region being mapped. The method presented here has an estimate of the order $O(n)$, making it an approach of choice in many situations. The performance of the algorithm is illustrated by several numerical examples.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121638045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 61
Analysis of a recursive least-squares signal-processing algorithm 递归最小二乘信号处理算法分析
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910027
F. Luk, S. Qiao
{"title":"Analysis of a recursive least-squares signal-processing algorithm","authors":"F. Luk, S. Qiao","doi":"10.1137/0910027","DOIUrl":"https://doi.org/10.1137/0910027","url":null,"abstract":"This paper concerns a popular recursive least-squares algorithm for beamforming. The way in which the method's stability depends on the condition of a special matrix is analyzed in detail, and a new procedure for estimating the error in the computed solution is presented.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124441113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Approximate Schur complement reconditioners on serial and parallel computers 串行和并行计算机上的近似舒尔补校正器
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910037
H. Elman
{"title":"Approximate Schur complement reconditioners on serial and parallel computers","authors":"H. Elman","doi":"10.1137/0910037","DOIUrl":"https://doi.org/10.1137/0910037","url":null,"abstract":"A class of preconditioning techniques for sparse matrices is considered, based on computing an approximation of the Schur complement of a (suitably ordered) matrix. The techniques generalize the reduced system methodology for 2-cyclic matrices to non-2-cyclic matrices, and in addition, they are well suited to parallel architectures. Their effectiveness with numerical experiments on a nine-point finite-difference operator is demonstrated, and an analysis showing that they can be implemented efficiently on multiprocessors is presented.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125254083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Linear and nonlinear acoustic wave propagation in the atmosphere 线性和非线性声波在大气中的传播
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910032
S. I. Hariharan, Yu Ping
{"title":"Linear and nonlinear acoustic wave propagation in the atmosphere","authors":"S. I. Hariharan, Yu Ping","doi":"10.1137/0910032","DOIUrl":"https://doi.org/10.1137/0910032","url":null,"abstract":"This paper describes the investigation of the acoustic wave-propagation theory and numerical implementation for the situation of an isothermal atmosphere. A one-dimensional model to validate an asymptotic theory and an axisymmetric three-dimensional situation to relate to a realistic situation are considered. In addition, nonlinear wave propagation and the numerical treatment are included. It is known that the gravitational effects play a crucial role in the low-frequency acoustic wave propagation. They propagate large distances and, as such, the numerical treatment of those problems becomes difficult in terms of posing boundary conditions that are valid for all frequencies. Our treatment is discussed in detail. Open questions are posed.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"321 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115836591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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