Topic
Minimum polynomial extrapolation
About: Minimum polynomial extrapolation is a research topic. Over the lifetime, 182 publications have been published within this topic receiving 5118 citations.
Papers published on a yearly basis
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 paper, a general methodology for multidimensional extrapolation is presented, which assumes a level set function exists which separates the region of known values from the region to be extrapolated, and it is shown that arbitrary orders of polynomial extrapolation can be formulated by simply solving a series of linear partial differential equations.
267 citations
TL;DR: It is shown that many of the existing extrapolation algorithms for noiseless observations are unified under the criterion of minimum norm least squares (MNLS) extrapolation, and some new algorithms useful for extrapolation and spectral estimation of band-limited sequences in one and two dimensions are presented.
Abstract: In this paper we present some new algorithms useful for extrapolation and spectral estimation of band-limited sequences in one and two dimensions. First we show that many of the existing extrapolation algorithms for noiseless observations are unified under the criterion of minimum norm least squares (MNLS) extrapolation. For example, the iterative algorithms proposed in [2] and [8]-[10] are shown to be special cases of a one-step gradient algorithm which has linear convergence. Convergence and other numerical properties are improved by going to a conjugate gradient algorithm. For noisy observations, these algorithms could be extended by considering a mean-square extrapolation criterion which gives rise to a mean-square extrapolation filter and also to a recursive extrapolation filter. Examples and application of these methods are given. Extension of these algorithms is made for problems where the signal is known to be periodic. A new set of functions called the periodic-discrete prolate spheroidal sequences (P-DPSS), analogous to DPSS [21], [22], are introduced and their properties are studied. Finally, several of these algorithms are generalized to two dimensions and the relevant equations are given.
253 citations
TL;DR: A new theory for joint order and stepsize control in extrapolation methods is presented, which defines a locally optimal order that can be determined along any trajectory to be computed.
Abstract: The paper presents a new theory for joint order and stepsize control in extrapolation methods. This theory defines a locally optimal order that can be determined along any trajectory to be computed. In addition, Shannon's information theory is applied to derive some ideal convergence model that is expected to describe the behavior of an extrapolation method over a large set of test problems. Extensive numerical comparisons document a drastic acceleration in stiff integration and a mild acceleration in non-stiff integration by the new device. Moreover, a significant increase in reliability, robustness, and portability of the extrapolation codes is achieved.
210 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 2 |
| 2016 | 6 |
| 2015 | 9 |
| 2014 | 7 |
| 2013 | 4 |
| 2012 | 8 |