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Sampling from Gauss Rules 从高斯规则中抽样
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909066
M. Evans, T. Swartz
{"title":"Sampling from Gauss Rules","authors":"M. Evans, T. Swartz","doi":"10.1137/0909066","DOIUrl":"https://doi.org/10.1137/0909066","url":null,"abstract":"Approximating multidimensional integrals via product quadrature rules becomes increasingly intractable as the dimension increases. Hammersley [Ann. New York Acad. Sci., 86 (1960), pp. 844–874] suggested sampling from product quadrature rules and Tsuda [Numer. Math., 20 (1973), pp. 377–391] considered this method using Fejer rules. In this paper we consider this approach using Gauss rules. Results are obtained concerning the variance of this form of sampling relative to sampling from the continuous distributions represented by the weight functions. It is shown that this approach can lead to variance reduction and its use is discussed in several examples.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122118505","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: 5
Implementation of the Topological $varepsilon $-Algorithm 拓扑varepsilon算法的实现
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909056
R. C. Tan
{"title":"Implementation of the Topological $varepsilon $-Algorithm","authors":"R. C. Tan","doi":"10.1137/0909056","DOIUrl":"https://doi.org/10.1137/0909056","url":null,"abstract":"A recent survey paper of D. A. Smith, W. F. Ford, and A. Sidi [SIAM Review, 29 (1987), pp. 199–233] found the topological $varepsilon $-algorithm (TEA) to compare very unfavourably with certain other methods for the acceleration of vector sequences. It is suggested that this poor performance of the TEA is due to an error in implementation. When this error is removed the method is found to perform at least as well as the other methods in most situations.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127764430","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: 13
How to Polish off Median Polish 如何去除中位数指甲油
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909064
A. Fink
{"title":"How to Polish off Median Polish","authors":"A. Fink","doi":"10.1137/0909064","DOIUrl":"https://doi.org/10.1137/0909064","url":null,"abstract":"Tukey's median polish is an algorithm for smoothing data in two-way tables. Each iteration lowers the $L_1 $ norm of the residual. For commensurable data the algorithm converges in a finite number of steps. It does not, in general, converge to the least $L_1 $ norm residual. We provide an algorithm that converges in a finite number of steps for any real data and gives the least $L_1 $ residual.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129095517","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: 6
Iterative Methods for Equality-Constrained Least Squares Problems 等式约束最小二乘问题的迭代方法
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909061
J. Barlow, N. Nichols, R. Plemmons
{"title":"Iterative Methods for Equality-Constrained Least Squares Problems","authors":"J. Barlow, N. Nichols, R. Plemmons","doi":"10.1137/0909061","DOIUrl":"https://doi.org/10.1137/0909061","url":null,"abstract":"We consider the linear equality-constrained least squares problem (LSE) of minimizing ${|c - Gx|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn–Tucker equations associated with the LSE problem.We show that our method is well suited for structural optimization problems in reliability analysis and optimal design. Numerical tests are performed on an Alliant FX/8 multiprocessor and a Cray-X-MP using some practical structural analysis data.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131891220","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: 41
Bit-Wise Behavior of Random Number Generators 随机数生成器的逐位行为
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909065
N. Altman
{"title":"Bit-Wise Behavior of Random Number Generators","authors":"N. Altman","doi":"10.1137/0909065","DOIUrl":"https://doi.org/10.1137/0909065","url":null,"abstract":"In 1985, G. Marsaglia proposed the m-tuple test, a runs test on bits, as a test of nonrandomness of a sequence of pseudorandom integers. We try this test on the outputs from a large set of pseudorandom number generators and discuss the behavior of the generators. The lower-order bits of a linear congruential generator taken modulo $2^p $ always have small period, and hence fail the test. However, we also show by example that sequences of bits with long period can display substantial nonrandom behavior. Linear congruential generators with prime modulus can fail the test in their low-order bits. Shift-register (Tausworthe) generators can fail in their central bits. The combination generators proposed by Marsaglia also fail the test.Fibonacci generators perform well on the test, if properly initialized. These generators require a vector of seeds which can be conveniently set using the output of a simple (that is, congruential or shift-register) generator. Shift-register generators are good initializers for almost every combination of lags and operators reported here. Fibonacci generators initialized by linear congruential generators pass if the initializer passes and fail if it fails.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127284002","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: 20
A Bisection Method for Measuring the Distance of a Stable Matrix to the Unstable Matrices 一种测量稳定矩阵到不稳定矩阵距离的二分法
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909059
R. Byers
{"title":"A Bisection Method for Measuring the Distance of a Stable Matrix to the Unstable Matrices","authors":"R. Byers","doi":"10.1137/0909059","DOIUrl":"https://doi.org/10.1137/0909059","url":null,"abstract":"We describe a bisection method to determine the 2-norm and Frobenius norm distances from a given matrix A to the nearest matrix with an eigenvalue on the imaginary axis. If A is stable in the sense that its eigenvalues lie in the open-left half plane, then this distance measures how “nearly unstable“ A is. Each step provides either a rigorous upper bound or a rigorous lower bound on the distance. A few bisection steps can bracket the distance within an order of magnitude. Bisection avoids the difficulties associated with nonlinear minimization techniques and the occasional failures associated with heuristic estimates. We show how the method might be used to estimate the distance to the nearest matrix with an eigenvalue on the unit circle.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121883346","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: 237
Far-Field Boundary Conditions for Time-Dependent Hyperbolic Systems 时变双曲系统的远场边界条件
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909054
B. Gustafsson
{"title":"Far-Field Boundary Conditions for Time-Dependent Hyperbolic Systems","authors":"B. Gustafsson","doi":"10.1137/0909054","DOIUrl":"https://doi.org/10.1137/0909054","url":null,"abstract":"We consider hyperbolic systems on an infinite domain. For computational reasons the domain is truncated and we develop boundary conditions at the far-field boundaries. The initial function is nonzero also outside the computational domain. The implementation is done such that instabilities are avoided. The conditions are applied to the Euler equations and numerical experiments are presented.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121533778","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: 42
Iteratively Reweighted Least Squares: Algorithms, Convergence Analysis, and Numerical Comparisons 迭代加权最小二乘:算法、收敛分析和数值比较
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909062
R. Wolke, H. Schwetlick
{"title":"Iteratively Reweighted Least Squares: Algorithms, Convergence Analysis, and Numerical Comparisons","authors":"R. Wolke, H. Schwetlick","doi":"10.1137/0909062","DOIUrl":"https://doi.org/10.1137/0909062","url":null,"abstract":"In solving robust linear regression problems, the parameter vector x, as well as an additional parameter s that scales the residuals, must be estimated simultaneously. A widely used method for doing so consists of first improving the scale parameter s for fixed x, and then improving x for fixed s by using a quadratic approximation to the objective function g. Since improving x is the expensive part of such algorithms, it makes sense to define the new scale s as a minimizes of g for fixed x. A strong global convergence analysis of this conceptual algorithm is given for a class of convex criterion functions and the so-called H- or W-approximations to g. Moreover, some appropriate finite and iterative subalgorithms for minimizing g with respect to s are discussed. Furthermore, the possibility of transforming the robust regression problem into a nonlinear least-squares problem is discussed. All algorithms described here were tested with a set of test problems, and the computational efficiency was compared wit...","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115162011","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: 199
On the Complexity of Sparse $QR$ and $LU$ Factorization of Finite-Element Matrices 有限元矩阵稀疏QR分解和LU分解的复杂性
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909057
A. George, E. Ng
{"title":"On the Complexity of Sparse $QR$ and $LU$ Factorization of Finite-Element Matrices","authors":"A. George, E. Ng","doi":"10.1137/0909057","DOIUrl":"https://doi.org/10.1137/0909057","url":null,"abstract":"Let A be an $n times n$ sparse nonsingular matrix derived from a two-dimensional finite-element mesh. If the matrix is symmetric and positive definite, and a nested dissection ordering is used, then the Cholesky factorization of A can be computed using $O(n^{{3 / 2}} )$ arithmetic operations, and the number of nonzeros in the Cholesky factor is $O(nlog n)$. In this article we show that the same complexity bounds can be attained when A is nonsymmetric and indefinite, and either Gaussian elimination with partial pivoting or orthogonal factorization is applied. Numerical experiments for a sequence of irregular mesh problems are provided.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127627810","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: 54
Diagonal Padé Approximations for Initial Value Problems 初值问题的对角逼近
Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI: 10.1137/0909055
M. Reusch, L. Ratzan, N. Pomphrey, W. Park
{"title":"Diagonal Padé Approximations for Initial Value Problems","authors":"M. Reusch, L. Ratzan, N. Pomphrey, W. Park","doi":"10.1137/0909055","DOIUrl":"https://doi.org/10.1137/0909055","url":null,"abstract":"Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128407780","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
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