Topic
Series (mathematics)
About: Series (mathematics) is a research topic. Over the lifetime, 31012 publications have been published within this topic receiving 625614 citations. The topic is also known as: mathematical series.
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TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
8,128 citations
6,036 citations
Book•
13 Dec 2005
TL;DR: This volume explores the differential evolution (DE) algorithm in both principle and practice and is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization.
Abstract: Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables.The differential evolution (DE) algorithm is a practical approach to global numerical optimization which is easy to understand, simple to implement, reliable, and fast. Packed with illustrations, computer code, new insights, and practical advice, this volume explores DE in both principle and practice. It is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization.
5,607 citations
Book•
19 Aug 2009
TL;DR: In this article, the mean and autocovariance functions of ARIMA models are estimated for multivariate time series and state-space models, and the spectral representation of the spectrum of a Stationary Process is inferred.
Abstract: 1 Stationary Time Series.- 2 Hilbert Spaces.- 3 Stationary ARMA Processes.- 4 The Spectral Representation of a Stationary Process.- 5 Prediction of Stationary Processes.- 6* Asymptotic Theory.- 7 Estimation of the Mean and the Autocovariance Function.- 8 Estimation for ARMA Models.- 9 Model Building and Forecasting with ARIMA Processes.- 10 Inference for the Spectrum of a Stationary Process.- 11 Multivariate Time Series.- 12 State-Space Models and the Kalman Recursions.- 13 Further Topics.- Appendix: Data Sets.
5,260 citations
4,700 citations