Download or read book Least Squares Optimal Approximation Simulation Techniques written by Peter Francis Salamon and published by . This book was released on 1973 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Least Square Optimal Approximation Simulation Techniques written by Peter Francis Salamon (Jr) and published by . This book was released on 1973 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report addresses the use of a quadratic objective function in an optimal control setting to construct an approximate solution for distributed parameter models. The systems are first order with respect to time and linear and time-dependent with respect to the spatial operator. The Least Squares variational technique is compared with the Galerkin finite element method in order to ascertain the worth of the optimal simulation on a digital computer. The Least Squares approach is demonstrated to be a powerful tool in simulating stable physical systems. In addition, the use of a coupled basis and a weighting matrix in the quadratic objective function can be used to tune the approximate solution. Thus, refined numerical simulations for certain classes of partial differential equations are readily accomplished with the Least Squares optimal simulation techniques. (Author).

Download or read book Least Squares Optimal Approximation Simulation Technique written by Peter Francis Salamon and published by . This book was released on 1973 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-12-01 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares: the principal tool for reducing the influence of errors when fitting models to given observations.

Download or read book Advances in Stochastic Simulation Methods written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a volume consisting of selected papers that were presented at the 3rd St. Petersburg Workshop on Simulation held at St. Petersburg, Russia, during June 28-July 3, 1998. The Workshop is a regular international event devoted to mathematical problems of simulation and applied statistics organized by the Department of Stochastic Simulation at St. Petersburg State University in cooperation with INFORMS College on Simulation (USA). Its main purpose is to exchange ideas between researchers from Russia and from the West as well as from other coun tries throughout the World. The 1st Workshop was held during May 24-28, 1994, and the 2nd workshop was held during June 18-21, 1996. The selected proceedings of the 2nd Workshop was published as a special issue of the Journal of Statistical Planning and Inference. Russian mathematical tradition has been formed by such genius as Tchebysh eff, Markov and Kolmogorov whose ideas have formed the basis for contempo rary probabilistic models. However, for many decades now, Russian scholars have been isolated from their colleagues in the West and as a result their mathe matical contributions have not been widely known. One of the primary reasons for these workshops is to bring the contributions of Russian scholars into lime light and we sincerely hope that this volume helps in this specific purpose.

Download or read book Recent Advances in Total Least Squares Techniques and Errors in variables Modeling written by Sabine van Huffel and published by SIAM. This book was released on 1997-01-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of the computational issues; statistical, numerical, and algebraic properties, and new generalizations and applications of advances on TLS and EIV models. Experts from several disciplines prepared overview papers which were presented at the conference and are included in this book.

Download or read book Least Squares written by Fouad Sabry and published by One Billion Knowledgeable. This book was released on 2024-05-11 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is Least Squares The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals made in the results of each individual equation. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Least squares Chapter 2: Gauss-Markov theorem Chapter 3: Regression analysis Chapter 4: Ridge regression Chapter 5: Total least squares Chapter 6: Ordinary least squares Chapter 7: Weighted least squares Chapter 8: Simple linear regression Chapter 9: Generalized least squares Chapter 10: Linear least squares (II) Answering the public top questions about least squares. (III) Real world examples for the usage of least squares in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Least Squares.

Download or read book Total Least Squares and Errors in Variables Modeling written by S. van Huffel and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: In response to a growing interest in Total Least Squares (TLS) and Errors-In-Variables (EIV) modeling by researchers and practitioners, well-known experts from several disciplines were invited to prepare an overview paper and present it at the third international workshop on TLS and EIV modeling held in Leuven, Belgium, August 27-29, 2001. These invited papers, representing two-thirds of the book, together with a selection of other presented contributions yield a complete overview of the main scientific achievements since 1996 in TLS and Errors-In-Variables modeling. In this way, the book nicely completes two earlier books on TLS (SIAM 1991 and 1997). Not only computational issues, but also statistical, numerical, algebraic properties are described, as well as many new generalizations and applications. Being aware of the growing interest in these techniques, it is a strong belief that this book will aid and stimulate users to apply the new techniques and models correctly to their own practical problems.

Download or read book Exact and Approximate Modeling of Linear Systems written by Ivan Markovsky and published by SIAM. This book was released on 2006-01-01 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title elegantly introduces the behavioral approach to mathematical modeling, an approach that requires models to be viewed as sets of possible outcomes rather than to be a priori bound to particular representations. The authors discuss exact and approximate fitting of data by linear, bilinear, and quadratic static models and linear dynamic models, a formulation that enables readers to select the most suitable representation for a particular purpose. This book presents exact subspace-type and approximate optimization-based identification methods, as well as representation-free problem formulations, an overview of solution approaches, and software implementation. Readers will find an exposition of a wide variety of modeling problems starting from observed data. The presented theory leads to algorithms that are implemented in C language and in MATLAB.

Download or read book Global Total Least Squares written by Berend Roorda and published by . This book was released on 1995 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Exact and Approximate Modeling of Linear Systems written by Ivan Markovsky and published by SIAM. This book was released on 2006-01-31 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact and Approximate Modeling of Linear Systems: A Behavioral Approach elegantly introduces the behavioral approach to mathematical modeling, an approach that requires models to be viewed as sets of possible outcomes rather than to be a priori bound to particular representations. The authors discuss exact and approximate fitting of data by linear, bilinear, and quadratic static models and linear dynamic models, a formulation that enables readers to select the most suitable representation for a particular purpose. This book presents exact subspace-type and approximate optimization-based identification methods, as well as representation-free problem formulations, an overview of solution approaches, and software implementation. Readers will find an exposition of a wide variety of modeling problems starting from observed data. The presented theory leads to algorithms that are implemented in C language and in MATLAB.

Download or read book Low Rank Approximation written by Ivan Markovsky and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. Much of the text is devoted to describing the applications of the theory including: system and control theory; signal processing; computer algebra for approximate factorization and common divisor computation; computer vision for image deblurring and segmentation; machine learning for information retrieval and clustering; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; and psychometrics for factor analysis. Software implementation of the methods is given, making the theory directly applicable in practice. All numerical examples are included in demonstration files giving hands-on experience and exercises and MATLAB® examples assist in the assimilation of the theory.

Download or read book Least squares Methods for Computational Electromagnetics written by Tzanio Valentinov Kolev and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The modeling of electromagnetic phenomena described by the Maxwell's equations is of critical importance in many practical applications. The numerical simulation of these equations is challenging and much more involved than initially believed. Consequently, many discretization techniques, most of them quite complicated, have been proposed. In this dissertation, we present and analyze a new methodology for approximation of the time-harmonic Maxwell's equations. It is an extension of the negative-norm least-squares finite element approach which has been applied successfully to a variety of other problems. The main advantages of our method are that it uses simple, piecewise polynomial, finite element spaces, while giving quasi-optimal approximation, even for solutions with low regularity (such as the ones found in practical applications). The numerical solution can be efficiently computed using standard and well-known tools, such as iterative methods and eigensolvers for symmetric and positive definite systems (e.g. PCG and LOBPCG) and reconditioners for second-order problems (e.g. Multigrid). Additionally, approximation of varying polynomial degrees is allowed and spurious eigenmodes are provably avoided. We consider the following problems related to the Maxwell's equations in the frequency domain: the magnetostatic problem, the electrostatic problem, the eigenvalue problem and the full time-harmonic system. For each of these problems, we present a natural (very) weak variational formulation assuming minimal regularity of the solution. In each case, we prove error estimates for the approximation with two different discrete least-squares methods. We also show how to deal with problems posed on domains that are multiply connected or have multiple boundary components. Besides the theoretical analysis of the methods, the dissertation provides various numerical results in two and three dimensions that illustrate and support the theory.

Download or read book Research in Progress written by and published by . This book was released on 1973 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Simulation based Approximate Solution of Large scale Linear Least Squares Problems and Applications written by Mengdi Wang and published by . This book was released on 2010 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider linear least squares problems, or linear systems that can be formulated into least squares problems, of very large dimension, such as those arising for example in dynamic programming (DP) and inverse problems. We introduce an associated approximate problem, within a subspace spanned by a relatively small number of basis functions, and solution methods that use simulation, importance sampling, and low-dimensional calculations. The main components of this methodology are a regression/ regularization approach that can deal with nearly singular problems, and an importance sampling design approach that exploits existing continuity structures in the underlying models, and allows the solution of very large problems. We also investigate the use of our regression/regularization approach in temporal difference-type methods in the context of approximate DP. Finally we demonstrate the application of our methodology in a series of practical large-scale examples arising from Fredholm integral equations of the first kind.

Download or read book Simulation Techniques in Financial Risk Management written by Ngai Hang Chan and published by John Wiley & Sons. This book was released on 2015-04-22 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition “...a nice, self-contained introduction to simulation and computational techniques in finance...” – Mathematical Reviews Simulation Techniques in Financial Risk Management, Second Edition takes a unique approach to the field of simulations by focusing on techniques necessary in the fields of finance and risk management. Thoroughly updated, the new edition expands on several key topics in these areas and presents many of the recent innovations in simulations and risk management, such as advanced option pricing models beyond the Black–Scholes paradigm, interest rate models, MCMC methods including stochastic volatility models simulations, model assets and model-free properties, jump diffusion, and state space modeling. The Second Edition also features: Updates to primary software used throughout the book, Microsoft Office® Excel® VBA New topical coverage on multiple assets, model-free properties, and related models More than 300 exercises at the end of each chapter, with select answers in the appendix, to help readers apply new concepts and test their understanding Extensive use of examples to illustrate how to use simulation techniques in risk management Practical case studies, such as the pricing of exotic options; simulations of Greeks in hedging; and the use of Bayesian ideas to assess the impact of jumps, so readers can reproduce the results of the studies A related website with additional solutions to problems within the book as well as Excel VBA and S-Plus computer code for many of the examples within the book Simulation Techniques in Financial Risk Management, Second Edition is an invaluable resource for risk managers in the financial and actuarial industries as well as a useful reference for readers interested in learning how to better gauge risk and make more informed decisions. The book is also ideal for upper-undergraduate and graduate-level courses in simulation and risk management.

Download or read book The Circuits and Filters Handbook written by Wai-Kai Chen and published by CRC Press. This book was released on 2002-12-23 with total page 3076 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bestseller in its first edition, The Circuits and Filters Handbook has been thoroughly updated to provide the most current, most comprehensive information available in both the classical and emerging fields of circuits and filters, both analog and digital. This edition contains 29 new chapters, with significant additions in the areas of computer-