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An efficient trust region algorithm for minimizing nondifferentiable composite functions 最小化不可微复合函数的有效信赖域算法
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910036
Eiki Yamakawa, M. Fukushima
{"title":"An efficient trust region algorithm for minimizing nondifferentiable composite functions","authors":"Eiki Yamakawa, M. Fukushima","doi":"10.1137/0910036","DOIUrl":"https://doi.org/10.1137/0910036","url":null,"abstract":"This paper presents a trust region algorithm for solving the following problem. Minimize $phi (x) = f(x) + h(c(x))$ over $x in R^n $, where f and c are smooth functions and h is a polyhedral convex function. Problems of this form include various important applications such as min-max optimization, Chebyshev approximation, and minimization of exact penalty functions in nonlinear programming. The algorithm is an adaptation of a recently proposed successive quadratic programming method for nonlinear programming and makes use of the second-order approximations to both f and c in order to avoid the Maratos effect. It is proved under appropriate assumptions that the algorithm is globally and quadratically convergent to a solution of the problem. Some numerical results exhibiting the effectiveness of the algorithm are also reported.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"28 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":"124085752","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: 7
Distribution of the average power of a normal time series 正态时间序列的平均幂分布
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910029
C. Helstrom
{"title":"Distribution of the average power of a normal time series","authors":"C. Helstrom","doi":"10.1137/0910029","DOIUrl":"https://doi.org/10.1137/0910029","url":null,"abstract":"The distribution of the sum of the squares of N correlated and normally distributed elements of a time series can be computed by numerical quadrature of a Laplace inversion integral involving the moment generating function (m.g.f.) of the sum. A method is presented for computing that m.g.f. for a stationary autoregressive moving-average (ARMA) process whose spectral density is a known rational function with $2n$ poles. It requires evaluating determinants of $2n times 2n$ and $(2n + 1) times (2n + 1)$ matrices, which may be much smaller than the $N times N$ covariance matrix of the time series. A second method is described that is based on the Kalman equations and applies to time series, possibly nonstationary, generated by a discrete-time linear system driven by normal random noise. A third method, utilizing the Levinson algorithm, applies when the time series is merely stationary.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"29 35","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120835620","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: 4
On collocation implementation for singularly perturbed two-point problems 奇异摄动两点问题的配置实现
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910034
U. Ascher, S. Jacobs
{"title":"On collocation implementation for singularly perturbed two-point problems","authors":"U. Ascher, S. Jacobs","doi":"10.1137/0910034","DOIUrl":"https://doi.org/10.1137/0910034","url":null,"abstract":"The numerical solution of singularly perturbed two-point boundary value problems in ordinary differential equations is considered. Implementation methods for general-purpose solvers of first-order linear systems are examined, with the basic difference scheme being collocation at Gaussian points. Adaptive mesh selection is based on localized error estimates at the collocation points These methods are implemented as modifications to the successful collocation code COLSYS, which was originally designed for mildly stiff problems only. Efficient high-order approximations to extremely stiff problems are obtained, and comparisons to COLSYS show that the modifications work relatively much better as the singular perturbation parameter gets small (i.e., the problem gets stiff), for both boundary-layer and turning-point problems.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"8 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":"125542066","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
Symmetric prime factor fast fourier transform algorithms 对称质因数快速傅里叶变换算法
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910028
J. S. Otto
{"title":"Symmetric prime factor fast fourier transform algorithms","authors":"J. S. Otto","doi":"10.1137/0910028","DOIUrl":"https://doi.org/10.1137/0910028","url":null,"abstract":"The prime factor algorithm (PFA) is a fast algorithm for the evaluation of the discrete Fourier transform (DFT), applicable when the sequence length N is a product of relative primes. PFAs are presented that take advantage of the symmetry in a real-even or real-odd sequence. These algorithms require only one-fourth the real arithmetic and storage requirements of the complex PFA. As with existing state-of-the-art PFAs, these algorithms can be performed in-place and in-order.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"51 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":"124121519","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: 3
Resolution of reconstruction methods in computerized tomography 计算机断层扫描重建方法的分辨率
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-05-01 DOI: 10.1137/0910030
Herman Kruse
{"title":"Resolution of reconstruction methods in computerized tomography","authors":"Herman Kruse","doi":"10.1137/0910030","DOIUrl":"https://doi.org/10.1137/0910030","url":null,"abstract":"The essential step in many reconstruction methods is the evaluation of certain integrals by the trapezoidal rule, using the data function $Rf$ and a weight function q. Hence the accuracy of the reconstruction depends on the accuracy of the trapezoidal rule and thus on the number and location of the points where the data are sampled. In parallel geometry Lindgren and Rattey have suggested using a grid that contains only 50 percent of the points of the standard grid. Using a special error estimate for the trapezoidal rule, it can be shown that to reconstruct details of a certain size the filtered backprojection method needs only the data on the small grid. Similar results can be obtained for fan-beam geometry; in this case Marr's algorithm successfully works on a small grid.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"164 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":"115043023","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: 24
A one-sided Jacobi algorithm for computing the singular value decomposition on avector computer 在矢量计算机上计算奇异值分解的单边Jacobi算法
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-03-01 DOI: 10.1137/0910023
P. de Rijk
{"title":"A one-sided Jacobi algorithm for computing the singular value decomposition on avector computer","authors":"P. de Rijk","doi":"10.1137/0910023","DOIUrl":"https://doi.org/10.1137/0910023","url":null,"abstract":"An old algorithm for computing the singular value decomposition, which was first mentioned by Hestenes [SIAM J. Appl. Math., 6 (1958), pp. 51–90], has gained renewed interest because of its properties of parallelism and vectorizability. Some computational modifications are given and a comparison with the well-known Golub–Reinsch algorithm is made. Comparative experiments on a CYBER 205 are reported.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124898420","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: 73
A New Method for Solving Triangular Systems on Distributed Memory Message-Passing Multiprocessors 分布式内存消息传递多处理器上求解三角系统的新方法
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-03-01 DOI: 10.1137/0910025
Guangye Li, T. Coleman
{"title":"A New Method for Solving Triangular Systems on Distributed Memory Message-Passing Multiprocessors","authors":"Guangye Li, T. Coleman","doi":"10.1137/0910025","DOIUrl":"https://doi.org/10.1137/0910025","url":null,"abstract":"Efficient triangular solvers for use on message passing multiprocessors are required, in several contexts, under the assumption that the matrix is distributed by columns (or rows) in a wrap fashion. In this paper we describe a new efficient parallel triangular solver for this problem. This new algorithm is based on the previous method of Li and Coleman [1986] but is considerably more efficient when $frac{n}{p}$ is relatively modest, where $p$ is the number of processors and $n$ is the problem dimension. A useful theoretical analysis is provided as well as extensive numerical results obtained on an Intel iPSC with $p leq 128$.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132267806","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: 79
Adaptive implicit criteria for two-phase flow with gravity and capillary pressure 考虑重力和毛细压力的两相流自适应隐式准则
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-03-01 DOI: 10.1137/0910017
P. Forsyth
{"title":"Adaptive implicit criteria for two-phase flow with gravity and capillary pressure","authors":"P. Forsyth","doi":"10.1137/0910017","DOIUrl":"https://doi.org/10.1137/0910017","url":null,"abstract":"Based on monotonicity conditions, the switching criteria for an adaptive implicit discretization for two-phase flow in a porous medium with gravity and capillary pressure are derived. These criteria can be applied to ultidimensional flows, provided an easily checked condition is satisfied. Use of the monotonicity conditions is demonstrated for some example problems in one and two dimensions.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121330399","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: 31
A total variation diminishing-projection method for solving implicit numerical schemes for scalar conservation laws: a numerical study of a simple case 求解标量守恒律隐式数值格式的全变差消投影法:一个简单情况的数值研究
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-03-01 DOI: 10.1137/0910018
A. Bourgeat, Bernardo Cockburn
{"title":"A total variation diminishing-projection method for solving implicit numerical schemes for scalar conservation laws: a numerical study of a simple case","authors":"A. Bourgeat, Bernardo Cockburn","doi":"10.1137/0910018","DOIUrl":"https://doi.org/10.1137/0910018","url":null,"abstract":"The stability of Newton’s method applied to implicit numerical schemes for scalar conservation laws requires, in the general case, an upper bound on the size of the timesteps. A simple locally defined projection, a total variation diminishing (TVD)-projection, is introduced, and it is used to obtain always-stable extensions of Newton’s method. A numerical study of this method applied to Godunov’s implicit scheme is presented.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131232853","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: 2
A Study of the Vortex Sheet Method and its Rate of Convergence 涡片法及其收敛速度的研究
Siam Journal on Scientific and Statistical Computing Pub Date : 1989-03-01 DOI: 10.1137/0910020
E. Puckett
{"title":"A Study of the Vortex Sheet Method and its Rate of Convergence","authors":"E. Puckett","doi":"10.1137/0910020","DOIUrl":"https://doi.org/10.1137/0910020","url":null,"abstract":"The subject of this study is Chorin's vortex sheet method, which is used to solve the Prandtl boundary layer equations and to impose the no-slip boundary condition in the random vortex method solution of the Navier–Stokes equations. This is a particle method in which the particles carry concentrations of vorticity and undergo a random walk to approximate the diffusion of vorticity in the boundary layer. During the random walk, particles are created at the boundary in order to satisfy the no-slip boundary condition. It is proved that in each of the $L^1 $, $L^2 $, and $L^infty $ norms the random walk and particle creation, taken together, provide a consistent approximation to the heat equation, subject to the no-slip boundary condition. Furthermore, it is shown that the truncation error is entirely due to the failure to satisfy the no-slip boundary condition exactly. It is demonstrated numerically that the method converges when it is used to model Blasius flow, and rates of convergence are established in terms of the computational parameters. The numerical study reveals that errors grow when the sheet length tends to zero much faster than the maximum sheet strength. The effectiveness of second-order time discretization, sheet tagging, and an alternative particle-creation algorithm are also examined.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133840487","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: 35
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