General linear methods

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  • In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding.

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  • n mathematics, an ordinary differential equation (abbreviated ODE) is an equation containing a function of one independent variable and its derivatives. There are many general forms an ODE can take, and these are classified in practice (see below).[1][2] The derivatives are ordinary because partial derivatives only apply to functions of many independent variables (see Partial differential equation).

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  • In this paper, we propose a novel method for semi-supervised learning of nonprojective log-linear dependency parsers using directly expressed linguistic prior knowledge (e.g. a noun’s parent is often a verb). Model parameters are estimated using a generalized expectation (GE) objective function that penalizes the mismatch between model predictions and linguistic expectation constraints.

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  • Lecture 8 - FIR Filter Design include all of the following content: FIR filter design, commonly used windows, generalized linear-phase FIR filter, the Kaiser window filter design method.

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  • This paper presents a semi-supervised training method for linear-chain conditional random fields that makes use of labeled features rather than labeled instances. This is accomplished by using generalized expectation criteria to express a preference for parameter settings in which the model’s distribution on unlabeled data matches a target distribution. We induce target conditional probability distributions of labels given features from both annotated feature occurrences in context and adhoc feature majority label assignment. ...

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  • Lecture "Advanced Econometrics (Part II) - Chapter 13: Generalized method of moments (GMM)" presentation of content: Orthogonality condition, method of moments, generalized method of moments, GMM and other estimators in the linear models, the advantages of GMM estimator, GMM estimation procedure.

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  • Over the past three decades, information in the aerospace and mechanical engineering fields in general and turbomachinery in particular has grown at an exponential rate. Fluid Dynamics and Heat Transfer of Turbomachinery is the first book, in one complete volume, to bring together the modern approaches and advances in the field, providing the most up-to-date, unified treatment available on basic principles, physical aspects of the aerothermal field, analysis, performance, theory, and computation of turbomachinery flow and heat transfer....

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  • One approach for estimation of independent component analysis (ICA) consists of using higher-order cumulant tensor. Tensors can be considered as generalization of matrices, or linear operators. Cumulant tensors are then generalizations of the covariance matrix. The covariance matrix is the second-order cumulant tensor, and the fourth order tensor is defined by the fourth-order cumulants cum(xi xj xk xl ).

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  • A system of linear equations is called sparse if only a relatively small number of its matrix elements aij are nonzero. It is wasteful to use general methods of linear algebra on such problems, because most of the O(N 3 ) arithmetic operations devoted to solving the set of equations or inverting the matrix involve zero operands. Furthermore, you might wish to work problems so large as to tax your available memory space, and it is wasteful to reserve storage for unfruitful zero elements.

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  • A FUNCTIONAL-ANALYTIC METHOD FOR THE STUDY OF DIFFERENCE EQUATIONS EUGENIA N. PETROPOULOU AND PANAYIOTIS D. SIAFARIKAS Received 29 October 2003 and in revised form 10 February 2004 We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the 1 and 2 p p spaces, p ∈ N, p ≥ 1.

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  • Changing time, timely change, change creating time, time measuring changeÐthe themes of this book are change and time in various per- mutations and combinations. The book also deals with nonlinearity, chaos, randomness, and stochastic models, the use of computers to study complicated systems of di¨erential equations, systems theory, complemen- tarity, the importance of formal models, methods from physics and mathe- matics for the analysis of cognitive systems, and interdisciplinarity, among other topics.

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  • This text is intended to provide an introduction to the standard methods that are used for the solution of first-order partial differential equations. Some of these ideas are likely to be introduced, probably in a course on mathematical methods during the second year of a degree programme with, perhaps, more detail in a third year. The material has been written to provide a general – but broad – introduction to the relevant ideas, and not as a text closely linked to a specific module or course of study. Indeed, the intention is to present the material so that it can be used as an...

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  • In the last 10 years, many advances have been made in the statistical modelling of time series data on air pollution and health. Standard regression methods used initially have been almost fully replaced by semi-parametric approaches (Speckman, 1988; Hastie and Tibshirani, 1990; Green and Silverman, 1994) such as Generalized linear models (GLM) with regression splines (McCullagh and Nelder, 1989), Generalized additive models (GAM) with non-parametric splines (Hastie and Tibshirani, 1990) and GAM with penalized splines (Marx and Eilers, 1998).

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  • This lecture will teach you how to fit nonlinear functions by using bases functions and how to control model complexity. The goal is for you to: Learn how to derive ridge regression; understand the trade-off of fitting the data and regularizing it; Learn polynomial regression; understand that, if basis functions are given, the problem of learning the parameters is still linear; learn cross-validation; understand model complexity and generalization.

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  • Generalized Method of Moments and Minimum Distance Estimation In Chapter 8 we saw how the generalized method of moments (GMM) approach to estimation can be applied to multiple-equation linear models, including systems of equations, with exogenous or endogenous explanatory variables, and to panel data models.

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  • Introduction to Adaptive Filters 18.1 18.2 18.3 18.4 18.5 What is an Adaptive Filter? The Adaptive Filtering Problem Filter Structures The Task of an Adaptive Filter Applications of Adaptive Filters System Identification • Inverse Modeling • Linear Prediction • Feedforward Control General Form of Adaptive FIR Algorithms • The MeanSquared Error Cost Function • The Wiener Solution • The Method of Steepest Descent • The LMS Algorithm • Other Stochastic Gradient Algorithms • Finite-Precision Effects and Other Implementation Issues • System Identification Example 18.

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  • Chapter 6 NON-LINEAR TAKESHI AMEMIYA Although economic theory generally provides only loose restrictions on the distribution of observable quantities, much econometric work is based on tightly specified parametric models and likelihood based methods of inference.

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  • Cable Force Adjustment and Construction Control 58.1 58.2 Introduction Determination of Designed Cable Forces Simply Supported Beam Method • Method of Continuous Beam on Rigid Supports • Optimization Method • Example 58 58.3 Adjustment of the Cable Forces General • Influence Matrix of the Cable Forces • Linear Programming Method • Order of Cable Adjustment 58.4 Simulation of Construction Process General • Forward Assemblage Analysis • Backward Disassemblage Analysis Danjian Han South China University of Technology 58.

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  • ICA by Tensorial Methods One approach for estimation of independent component analysis (ICA) consists of using higher-order cumulant tensor. Tensors can be considered as generalization of matrices, or linear operators. Cumulant tensors are then generalizations of the covariance matrix. The covariance matrix is the second-order cumulant tensor, and the fourth order tensor is defined by the fourth-order cumulants cum(xi xj xk xl ). For an introduction to cumulants, see Section 2.7.

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  • A composition procedure for linear and nondeleting extended top-down tree transducers is presented. It is demonstrated that the new procedure is more widely applicable than the existing methods. In general, the result of the composition is an extended top-down tree transducer that is no longer linear or nondeleting, but in a number of cases these properties can easily be recovered by a post-processing step.

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