Topic
Sequence transformation
About: Sequence transformation is a research topic. Over the lifetime, 215 publications have been published within this topic receiving 6775 citations.
Papers published on a yearly basis
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Papers
Book•
5 Dec 1991
TL;DR: This chapter discusses the construction of Extrapolation Processes, as well as generalizations of the -algorithm, and some of the algorithms used in this process.
Abstract: Introduction to the Theory. First Steps. What is an Extrapolation Method? What is an Extrapolation Algorithm? Quasi-linear Sequence Transformations. Sequence Transformations as Ratios of Determinants. Triangular Recursive Schemes. Normal Forms of the Algorithms. Progressive Forms of the Algorithms. Particular Rules of the Algorithms. Accelerability and Non-accelerability. Optimality. Asymptotic Behaviour of Sequences. Scalar Extrapolation Algorithms. The E-algorithm. Richardson Extrapolation Process. The -algorithm. The G-transformation. Rational Extrapolation. Generalizations of the -algorithm. Levin's Transformations. Overholt's Process. -type Algorithms. The Iterated 2 Process. Miscellaneous Algorithms. Special Devices. Error Estimates and Acceleration. Convergence Tests and Acceleration. Construction of Asymptotic Expansions. Construction of Extrapolation Processes. Extraction Procedures. Automatic Selection. Composite Sequence Transformations. Error Control. Contractive Sequence Transformations. Least Squares Extrapolation. Vector Extrapolation Algorithms. The Vector -algorithm. The Topological -algorithm. The Vector E-algorithm. The Recursive Projection Algorithm. The H-algorithm. The Ford-Sidi Algorithms. Miscellaneous Algorithms. Continuous Prediction Algorithms. The Taylor Expansion. Confluent Overholt's process. Confluent -algorithms. Confluent -algorithm. Confluent G-transform. Confluent E-algorithm. -type Confluent Algorithms. Applications. Sequences and Series: Simple Sequences, Double Sequences, Chebyshev and Fourier Series, Continued Fractions, Vector Sequences. Systems of Equations: Linear Systems, Projection Methods, Regularization and Penalty Techniques, Nonlinear Equations, Continuation Methods. Eigenelements: Eigenvalues and eigenvectors, Derivatives of Eigensystems. Integral and Differential Equations: Implicit Runge-Kutta Methods, Boundary Value Problems, Nonlinear Methods, Laplace Transform Inversion, Partial Differential Equations. Interpolation and Approximation. Statistics: The Jackknife, ARMA Models, Monte-Carlo Methods. Integration and Differentiation: Acceleration of Quadrature Formulae, Nonlinear Quadrature Formulae, Cauchy's Principal Values, Infinite Integrals, Multiple Integrals, Numerical Differentiation. Prediction. Software. Programming the Algorithms. Computer Arithmetic. Programs. Bibliography. Index.
503 citations
TL;DR: In this article, a large number of mainly nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series are discussed and the theoretical properties of the sequence transformations in convergence acceleration and summation processes are analyzed.
434 citations
330 citations
Patent•
7 Nov 1997
TL;DR: In this article, a transformation description language (TDL) is proposed for specifying how data is to be manipulated in a data warehousing application. The TDL is comprised of a source for storing raw data, one or more transformation objects for processing the raw data according to predefined instructions, and a target for storing the processed data.
Abstract: A transformation description language (TDL) for specifying how data is to be manipulated in a data warehousing application. The TDL is comprised of a source for storing raw data, one or more transformation objects for processing the raw data according to predefined instructions, and a target for storing the processed data. A mapping is used for directing the data flow between the I/O ports corresponding to the source, the plurality of transformation objects, and the target. The mapping specifies the connectivity between the source, transformation, and target objects as well as the order of these connections. There are a number of different transformations which can be performed to manipulate the data. Some such transformations include: an aggregator transformation, an expression transformation, a filter transformation, a lookup transformation, a query transformation, a sequence transformation, a stored procedure transformation, and an update strategy transformation.
291 citations
TL;DR: In this paper, the Wynn rho algorithm was compared to Salzer summation in numerical inversion of Laplace transform and only one nonlinear method was found to be superior.
Abstract: The sequence of Gaver functionals is useful in the numerical inversion of Laplace transforms. The convergence behavior of the sequence is logarithmic, therefore, an acceleration scheme is required. The accepted procedure utilizes Salzer summation, because in many cases the Gaver functionals have the asymptotic behavior @?"n(t) - @?"n(t) ~ An^-^2 as n -> ~ for fixed t. It seems that no other acceleration schemes have been investigated in this area. Surely, the popular nonlinear methods should be more effective. However, to our surprise, only one nonlinear method was superior to Salzer summation, namely the Wynn rho algorithm.
266 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 3 |
| 2019 | 6 |
| 2018 | 4 |
| 2017 | 3 |
| 2016 | 8 |