Point Estimation Of Root Finding Methods
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Point Estimation Of Root Finding Methods
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Author : Miodrag Petkovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-29
Point Estimation Of Root Finding Methods written by Miodrag Petkovic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-29 with Mathematics categories.
This book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale's point estimation theory, introduced in 1986. Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. The remaining chapters contain the recent author's results on initial conditions guaranteing convergence of a wide class of iterative methods for solving algebraic equations. These conditions are of practical interest since they depend only on available data, the information of a function whose zeros are sought and initial approximations. The convergence approach presented can be applied in designing a package for the simultaneous approximation of polynomial zeros.
Multipoint Methods For Solving Nonlinear Equations
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Author : Miodrag Petkovic
language : en
Publisher: Academic Press
Release Date : 2012-12-31
Multipoint Methods For Solving Nonlinear Equations written by Miodrag Petkovic and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Technology & Engineering categories.
This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to wide a range of research areas along with many numerical examples for a deep understanding of the usefulness of each method. This book will make it possible for the researchers to tackle difficult problems and deepen their understanding of problem solving using numerical methods. Multipoint methods are of great practical importance, as they determine sequences of successive approximations for evaluative purposes. This is especially helpful in achieving the highest computational efficiency. The rapid development of digital computers and advanced computer arithmetic have provided a need for new methods useful to solving practical problems in a multitude of disciplines such as applied mathematics, computer science, engineering, physics, financial mathematics, and biology. - Provides a succinct way of implementing a wide range of useful and important numerical algorithms for solving research problems - Illustrates how numerical methods can be used to study problems which have applications in engineering and sciences, including signal processing, and control theory, and financial computation - Facilitates a deeper insight into the development of methods, numerical analysis of convergence rate, and very detailed analysis of computational efficiency - Provides a powerful means of learning by systematic experimentation with some of the many fascinating problems in science - Includes highly efficient algorithms convenient for the implementation into the most common computer algebra systems such as Mathematica, MatLab, and Maple
An Introduction To Numerical Methods And Analysis
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Author : James F. Epperson
language : en
Publisher: John Wiley & Sons
Release Date : 2021-07-21
An Introduction To Numerical Methods And Analysis written by James F. Epperson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Mathematics categories.
The new edition of the popular introductory textbook on numerical approximation methods and mathematical analysis, with a unique emphasis on real-world application An Introduction to Numerical Methods and Analysis helps students gain a solid understanding of a wide range of numerical approximation methods for solving problems of mathematical analysis. Designed for entry-level courses on the subject, this popular textbook maximizes teaching flexibility by first covering basic topics before gradually moving to more advanced material in each chapter and section. Throughout the text, students are provided clear and accessible guidance on a wide range of numerical methods and analysis techniques, including root-finding, numerical integration, interpolation, solution of systems of equations, and many others. This fully revised third edition contains new sections on higher-order difference methods, the bisection and inertia method for computing eigenvalues of a symmetric matrix, a completely re-written section on different methods for Poisson equations, and spectral methods for higher-dimensional problems. New problem sets—ranging in difficulty from simple computations to challenging derivations and proofs—are complemented by computer programming exercises, illustrative examples, and sample code. This acclaimed textbook: Explains how to both construct and evaluate approximations for accuracy and performance Covers both elementary concepts and tools and higher-level methods and solutions Features new and updated material reflecting new trends and applications in the field Contains an introduction to key concepts, a calculus review, an updated primer on computer arithmetic, a brief history of scientific computing, a survey of computer languages and software, and a revised literature review Includes an appendix of proofs of selected theorems and a companion website with additional exercises, application models, and supplemental resources An Introduction to Numerical Methods and Analysis, Third Edition is the perfect textbook for upper-level undergraduate students in mathematics, science, and engineering courses, as well as for courses in the social sciences, medicine, and business with numerical methods and analysis components.
Paris Princeton Lectures On Mathematical Finance 2010
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Author : Areski Cousin
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-29
Paris Princeton Lectures On Mathematical Finance 2010 written by Areski Cousin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-29 with Mathematics categories.
The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.
The Method Of Intrinsic Scaling
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Author : José Miguel Urbano
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-20
The Method Of Intrinsic Scaling written by José Miguel Urbano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-20 with Mathematics categories.
This set of lectures, which had its origin in a mini course delivered at the Summer Program of IMPA (Rio de Janeiro), is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular PDEs.In the first part, the theory is presented from scratch for the model case of the degenerate p-Laplace equation. The second part deals with three applications of the theory to relevant models arising from flows in porous media and phase transitions.
Information Theoretic Methods For Estimating Of Complicated Probability Distributions
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Author : Zhi Zong
language : en
Publisher: Elsevier
Release Date : 2006-08-15
Information Theoretic Methods For Estimating Of Complicated Probability Distributions written by Zhi Zong and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-15 with Mathematics categories.
Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC- density functions automatically determined from samples- Free of assuming density forms- Computation-effective methods suitable for PC
Mutational Analysis
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Author : Thomas Lorenz
language : en
Publisher: Springer
Release Date : 2010-05-29
Mutational Analysis written by Thomas Lorenz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-29 with Mathematics categories.
Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions, for example, do not have an obvious linear structure. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals. Here are some of the examples: - Feedback evolutions of compact subsets of the Euclidean space - Birth-and-growth processes of random sets (not necessarily convex) - Semilinear evolution equations - Nonlocal parabolic differential equations - Nonlinear transport equations for Radon measures - A structured population model - Stochastic differential equations with nonlocal sample dependence and how they can be coupled in systems immediately - due to the joint framework of Mutational Analysis. Finally, the book offers new tools for modelling.
Substitution Dynamical Systems Spectral Analysis
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Author : Martine Queffélec
language : en
Publisher: Springer
Release Date : 2010-01-30
Substitution Dynamical Systems Spectral Analysis written by Martine Queffélec and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-30 with Mathematics categories.
This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.
Generalized Linear Models
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Author : Jeff Gill
language : en
Publisher: SAGE Publications
Release Date : 2019-05-14
Generalized Linear Models written by Jeff Gill and has been published by SAGE Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-14 with Social Science categories.
Generalized Linear Models: A Unified Approach provides an introduction to and overview of GLMs, with each chapter carefully laying the groundwork for the next. The Second Edition provides examples using real data from multiple fields in the social sciences such as psychology, education, economics, and political science, including data on voting intentions in the 2016 U.S. Republican presidential primaries. The Second Edition also strengthens material on the exponential family form, including a new discussion on the multinomial distribution; adds more information on how to interpret results and make inferences in the chapter on estimation procedures; and has a new section on extensions to generalized linear models. Software scripts, supporting documentation, data for the examples, and some extended mathematical derivations are available on the authors’ websites as well as through the \texttt{R} package \texttt{GLMpack}. Supporting material (data and code) to replicate the examples in the book can be found in the ′GLMpack′ package on CRAN or on the website&
Potential Analysis Of Stable Processes And Its Extensions
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Author : Krzysztof Bogdan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-14
Potential Analysis Of Stable Processes And Its Extensions written by Krzysztof Bogdan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-14 with Mathematics categories.
Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schrödinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case. This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to non-specialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a CNRS/HARP Workshop, Angers 2006. The reader will gain insight into the modern theory of stable and related processes and their potential analysis with a theoretical motivation for the study of their fine properties.