Point Estimation Of Root Finding Methods

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Point Estimation of Root Finding Methods

Miodrag Petkovic
Point Estimation of Root Finding Methods Book PDF

Author : Miodrag Petkovic
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 51,5 Mb
Release : 2008-05-29
Category : Mathematics
ISBN : 9783540778509

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Point Estimation of Root Finding Methods by Miodrag Petkovic Pdf

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

Miodrag Petkovic,Beny Neta,Ljiljana Petkovic,Jovana Dzunic
Multipoint Methods for Solving Nonlinear Equations Book PDF

Author : Miodrag Petkovic,Beny Neta,Ljiljana Petkovic,Jovana Dzunic
Publisher : Academic Press
Page : 344 pages
File Size : 47,7 Mb
Release : 2012-12-31
Category : Mathematics
ISBN : 9780123972989

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Multipoint Methods for Solving Nonlinear Equations by Miodrag Petkovic,Beny Neta,Ljiljana Petkovic,Jovana Dzunic Pdf

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

Lectures on Symplectic Geometry

Ana Cannas da Silva
Lectures on Symplectic Geometry Book PDF

Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 50,6 Mb
Release : 2004-10-27
Category : Mathematics
ISBN : 9783540453307

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Lectures on Symplectic Geometry by Ana Cannas da Silva Pdf

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Polyharmonic Boundary Value Problems

Filippo Gazzola,Hans-Christoph Grunau,Guido Sweers
Polyharmonic Boundary Value Problems Book PDF

Author : Filippo Gazzola,Hans-Christoph Grunau,Guido Sweers
Publisher : Springer
Page : 423 pages
File Size : 44,5 Mb
Release : 2010-05-26
Category : Mathematics
ISBN : 9783642122453

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Polyharmonic Boundary Value Problems by Filippo Gazzola,Hans-Christoph Grunau,Guido Sweers Pdf

This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.

Enumerative Invariants in Algebraic Geometry and String Theory

Marcos Marino,Michael Thaddeus,Ravi Vakil
Enumerative Invariants in Algebraic Geometry and String Theory Book PDF

Author : Marcos Marino,Michael Thaddeus,Ravi Vakil
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 45,6 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783540798132

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Enumerative Invariants in Algebraic Geometry and String Theory by Marcos Marino,Michael Thaddeus,Ravi Vakil Pdf

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.

Quantum Transport

Gregoire Allaire,Anton Arnold,Pierre Degond,Thomas Y. Hou
Quantum Transport Book PDF

Author : Gregoire Allaire,Anton Arnold,Pierre Degond,Thomas Y. Hou
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 42,5 Mb
Release : 2008-08-13
Category : Mathematics
ISBN : 9783540795735

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Quantum Transport by Gregoire Allaire,Anton Arnold,Pierre Degond,Thomas Y. Hou Pdf

In this volume, a result of The CIME Summer School held in Cetraro, Italy, in 2006, four leading specialists present different aspects of quantum transport modeling. It provides an excellent basis for researchers in this field.

Lévy Matters I

Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
L vy Matters I Book PDF

Author : Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
Publisher : Springer
Page : 206 pages
File Size : 52,7 Mb
Release : 2010-09-02
Category : Mathematics
ISBN : 9783642140075

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Lévy Matters I by Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab Pdf

Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.

Holomorphic Dynamical Systems

Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate
Holomorphic Dynamical Systems Book PDF

Author : Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 45,9 Mb
Release : 2010-07-31
Category : Mathematics
ISBN : 9783642131707

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Holomorphic Dynamical Systems by Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate Pdf

The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.

A Theory of Shape Identification

Frédéric Cao,José-Luis Lisani,Jean-Michel Morel,Pablo Musé,Frédéric Sur
A Theory of Shape Identification Book PDF

Author : Frédéric Cao,José-Luis Lisani,Jean-Michel Morel,Pablo Musé,Frédéric Sur
Publisher : Springer
Page : 260 pages
File Size : 50,6 Mb
Release : 2008-08-17
Category : Mathematics
ISBN : 9783540684817

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A Theory of Shape Identification by Frédéric Cao,José-Luis Lisani,Jean-Michel Morel,Pablo Musé,Frédéric Sur Pdf

Recent years have seen dramatic progress in shape recognition algorithms applied to ever-growing image databases. They have been applied to image stitching, stereo vision, image mosaics, solid object recognition and video or web image retrieval. More fundamentally, the ability of humans and animals to detect and recognize shapes is one of the enigmas of perception. The book describes a complete method that starts from a query image and an image database and yields a list of the images in the database containing shapes present in the query image. A false alarm number is associated to each detection. Many experiments will show that familiar simple shapes or images can reliably be identified with false alarm numbers ranging from 10-5 to less than 10-300. Technically speaking, there are two main issues. The first is extracting invariant shape descriptors from digital images. Indeed, a shape can be seen from various angles and distances and in various lights.

Séminaire de Probabilités XLIII

Catherine Donati Martin,Antoine Lejay,Alain Rouault
S minaire de Probabilit s XLIII Book PDF

Author : Catherine Donati Martin,Antoine Lejay,Alain Rouault
Publisher : Springer
Page : 503 pages
File Size : 48,9 Mb
Release : 2010-10-20
Category : Mathematics
ISBN : 9783642152177

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Séminaire de Probabilités XLIII by Catherine Donati Martin,Antoine Lejay,Alain Rouault Pdf

This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.

Pseudo-Differential Operators

Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft
Pseudo Differential Operators Book PDF

Author : Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft
Publisher : Springer
Page : 214 pages
File Size : 51,6 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9783540682684

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Pseudo-Differential Operators by Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft Pdf

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.

Mastering Python for Finance

James Ma Weiming
Mastering Python for Finance Book PDF

Author : James Ma Weiming
Publisher : Packt Publishing Ltd
Page : 340 pages
File Size : 47,5 Mb
Release : 2015-04-29
Category : Computers
ISBN : 9781784397876

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Mastering Python for Finance by James Ma Weiming Pdf

If you are an undergraduate or graduate student, a beginner to algorithmic development and research, or a software developer in the financial industry who is interested in using Python for quantitative methods in finance, this is the book for you. It would be helpful to have a bit of familiarity with basic Python usage, but no prior experience is required.

Topological Complexity of Smooth Random Functions

Robert Adler,Jonathan E. Taylor
Topological Complexity of Smooth Random Functions Book PDF

Author : Robert Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 40,6 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9783642195792

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Topological Complexity of Smooth Random Functions by Robert Adler,Jonathan E. Taylor Pdf

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.

Matrix Convolution Operators on Groups

Cho-Ho Chu
Matrix Convolution Operators on Groups Book PDF

Author : Cho-Ho Chu
Publisher : Springer
Page : 114 pages
File Size : 46,6 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9783540697985

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Matrix Convolution Operators on Groups by Cho-Ho Chu Pdf

In the last decade, convolution operators of matrix functions have received unusual attention due to their diverse applications. This monograph presents some new developments in the spectral theory of these operators. The setting is the Lp spaces of matrix-valued functions on locally compact groups. The focus is on the spectra and eigenspaces of convolution operators on these spaces, defined by matrix-valued measures. Among various spectral results, the L2-spectrum of such an operator is completely determined and as an application, the spectrum of a discrete Laplacian on a homogeneous graph is computed using this result. The contractivity properties of matrix convolution semigroups are studied and applications to harmonic functions on Lie groups and Riemannian symmetric spaces are discussed. An interesting feature is the presence of Jordan algebraic structures in matrix-harmonic functions.

Information Geometry

Khadiga Arwini,C. T. J. Dodson
Information Geometry Book PDF

Author : Khadiga Arwini,C. T. J. Dodson
Publisher : Springer
Page : 260 pages
File Size : 50,8 Mb
Release : 2008-07-19
Category : Mathematics
ISBN : 9783540693932

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Information Geometry by Khadiga Arwini,C. T. J. Dodson Pdf

This volume uses information geometry to give a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings, cryptology studies, clustering of communications and galaxies, and cosmological voids.