General linear methods

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 RungeKutta 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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(BQ) Part 2 book "An introduction to statistical methods and data analysis" has contents: Linear regression and correlation, multiple regression and the general linear model; further regression topics, analysis of variance for blocked designs, the analysis of covariance; analysis of variance for some unbalanced designs
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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 semisupervised learning of nonprojective loglinear 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 linearphase FIR filter, the Kaiser window filter design method.
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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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This paper presents a semisupervised training method for linearchain 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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(BQ) In the years since the fourth edition of this seminal work was published, active research has developed the Finite Element Method into the preeminent tool for the modeling of physical systems. Volume 2 of the "The finite element method" provides a complete introduction to the method and is essential reading for undergraduates, postgraduates and professional engineers.
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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 uptodate, 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 higherorder 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 secondorder cumulant tensor, and the fourth order tensor is deﬁned by the fourthorder 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 FUNCTIONALANALYTIC 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 functionalanalytic 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 firstorder 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 semiparametric 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 nonparametric 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 tradeoff 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 crossvalidation; understand model complexity and generalization.
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Nonhomogeneous ordinary differential equations can be solved if the general solution to the homogenous version is known, in which case the undetermined coefficients method or variation of parameters can be used to find the particular solution.
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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 multipleequation 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 • FinitePrecision Effects and Other Implementation Issues • System Identiﬁcation Example 18.
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Chapter 6 NONLINEAR 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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