Monte Carlo Methods Utilizing Mathematica

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Monte Carlo Methods Utilizing Mathematica®

Sujaul Chowdhury
Monte Carlo Methods Utilizing Mathematica Book PDF

Author : Sujaul Chowdhury
Publisher : Springer Nature
Page : 151 pages
File Size : 47,8 Mb
Release : 2023-02-23
Category : Mathematics
ISBN : 9783031232947

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Monte Carlo Methods Utilizing Mathematica® by Sujaul Chowdhury Pdf

This book provides practical demonstrations of how to carry out definite integrals with Monte Carlo methods using Mathematica. Random variates are sampled by the inverse transform method and the acceptance-rejection method using uniform, linear, Gaussian, and exponential probability distribution functions. A chapter on the application of the Variational Quantum Monte Carlo method to a simple harmonic oscillator is included. These topics are all essential for students of mathematics and physics. The author includes thorough background on each topic covered within the book in order to help readers understand the subject. The book also contains many examples to show how the methods can be applied.

Monte Carlo Methods

Sujaul Chowdhury
Monte Carlo Methods Book PDF

Author : Sujaul Chowdhury
Publisher : Springer Nature
Page : 123 pages
File Size : 53,8 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031024290

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Monte Carlo Methods by Sujaul Chowdhury Pdf

This book is intended for undergraduate students of Mathematics, Statistics, and Physics who know nothing about Monte Carlo Methods but wish to know how they work. All treatments have been done as much manually as is practicable. The treatments are deliberately manual to let the readers get the real feel of how Monte Carlo Methods work. Definite integrals of a total of five functions (), namely Sin(), Cos(), e, loge(), and 1/(1+2), have been evaluated using constant, linear, Gaussian, and exponential probability density functions (). It is shown that results agree with known exact values better if () is proportional to (). Deviation from the proportionality results in worse agreement. This book is on Monte Carlo Methods which are numerical methods for Computational Physics. These are parts of a syllabus for undergraduate students of Mathematics and Physics for the course titled "Computational Physics." Need for the book: Besides the three referenced books, this is the only book that teaches how basic Monte Carlo methods work. This book is much more explicit and easier to follow than the three referenced books. The two chapters on the Variational Quantum Monte Carlo method are additional contributions of the book. Pedagogical features: After a thorough acquaintance with background knowledge in Chapter 1, five thoroughly worked out examples on how to carry out Monte Carlo integration is included in Chapter 2. Moreover, the book contains two chapters on the Variational Quantum Monte Carlo method applied to a simple harmonic oscillator and a hydrogen atom. The book is a good read; it is intended to make readers adept at using the method. The book is intended to aid in hands-on learning of the Monte Carlo methods.

The Monte Carlo Method

Yu.A. Shreider
The Monte Carlo Method Book PDF

Author : Yu.A. Shreider
Publisher : Elsevier
Page : 396 pages
File Size : 42,6 Mb
Release : 2014-05-16
Category : Mathematics
ISBN : 9781483155579

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The Monte Carlo Method by Yu.A. Shreider Pdf

The Monte Carlo Method: The Method of Statistical Trials is a systematic account of the fundamental concepts and techniques of the Monte Carlo method, together with its range of applications. Some of these applications include the computation of definite integrals, neutron physics, and in the investigation of servicing processes. This volume is comprised of seven chapters and begins with an overview of the basic features of the Monte Carlo method and typical examples of its application to simple problems in computational mathematics. The next chapter examines the computation of multi-dimensional integrals using the Monte Carlo method. Some examples of statistical modeling of integrals are analyzed, together with the accuracy of the computations. Subsequent chapters focus on the applications of the Monte Carlo method in neutron physics; in the investigation of servicing processes; in communication theory; and in the generation of uniformly distributed random numbers on electronic computers. Methods for organizing statistical experiments on universal digital computers are discussed. This book is designed for a wide circle of readers, ranging from those who are interested in the fundamental applications of the Monte Carlo method, to those who are concerned with comparatively limited problems of the peculiarities of simulating physical processes.

The Monte Carlo Methods

Abdo Abou Jaoudé
The Monte Carlo Methods Book PDF

Author : Abdo Abou Jaoudé
Publisher : BoD – Books on Demand
Page : 234 pages
File Size : 47,6 Mb
Release : 2022-03-09
Category : Science
ISBN : 9781839687594

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The Monte Carlo Methods by Abdo Abou Jaoudé Pdf

In applied mathematics, the name Monte Carlo is given to the method of solving problems by means of experiments with random numbers. This name, after the casino at Monaco, was first applied around 1944 to the method of solving deterministic problems by reformulating them in terms of a problem with random elements, which could then be solved by large-scale sampling. But, by extension, the term has come to mean any simulation that uses random numbers. Monte Carlo methods have become among the most fundamental techniques of simulation in modern science. This book is an illustration of the use of Monte Carlo methods applied to solve specific problems in mathematics, engineering, physics, statistics, and science in general.

Monte Carlo Methods

J. Hammersley
Monte Carlo Methods Book PDF

Author : J. Hammersley
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 51,9 Mb
Release : 2013-03-07
Category : Science
ISBN : 9789400958197

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Monte Carlo Methods by J. Hammersley Pdf

This monograph surveys the present state of Monte Carlo methods. we have dallied with certain topics that have interested us Although personally, we hope that our coverage of the subject is reasonably complete; at least we believe that this book and the references in it come near to exhausting the present range of the subject. On the other hand, there are many loose ends; for example we mention various ideas for variance reduction that have never been seriously appli(:d in practice. This is inevitable, and typical of a subject that has remained in its infancy for twenty years or more. We are convinced Qf:ver theless that Monte Carlo methods will one day reach an impressive maturity. The main theoretical content of this book is in Chapter 5; some readers may like to begin with this chapter, referring back to Chapters 2 and 3 when necessary. Chapters 7 to 12 deal with applications of the Monte Carlo method in various fields, and can be read in any order. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient. We assume that the reader has what might roughly be described as a 'graduate' knowledge of mathematics. The actual mathematical techniques are, with few exceptions, quite elementary, but we have freely used vectors, matrices, and similar mathematical language for the sake of conciseness.

Numerical Exploration of Fourier Transform and Fourier Series

Sujaul Chowdhury,Abdullah Al Sakib
Numerical Exploration of Fourier Transform and Fourier Series Book PDF

Author : Sujaul Chowdhury,Abdullah Al Sakib
Publisher : Springer Nature
Page : 113 pages
File Size : 42,8 Mb
Release : 2023-08-01
Category : Science
ISBN : 9783031346644

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Numerical Exploration of Fourier Transform and Fourier Series by Sujaul Chowdhury,Abdullah Al Sakib Pdf

This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations. This book also contains numerical solution of differential equation of driven damped oscillator using 4th order Runge-Kutta method. Numerical solutions are compared with analytical solutions, and the behaviors of mechanical system are also depicted by plotting velocity versus displacement rather than displaying displacement as a function of time. This book is useful to physical science and engineering professionals who often need to obtain frequencies present in numerical data using the discrete Fourier transform. This book: Aids readers to numerically calculate or obtain frequencies that are present in numerical data Explores the use of the discrete Fourier transform and demonstrates practical numerical calculation Utilizes 4th order Runge-Kutta method and Mathematica for the numerical solution of differential equation

Lectures on Monte Carlo Methods

Neal Noah Madras
Lectures on Monte Carlo Methods Book PDF

Author : Neal Noah Madras
Publisher : Springer Science & Business
Page : 116 pages
File Size : 48,6 Mb
Release : 2002
Category : Mathematics
ISBN : 0821829785

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Lectures on Monte Carlo Methods by Neal Noah Madras Pdf

Monte Carlo methods form an experimental branch of mathematics that employs simulations driven by random number generators. These methods are often used when others fail, since they are much less sensitive to the ``curse of dimensionality'', which plagues deterministic methods in problems with a large number of variables. Monte Carlo methods are used in many fields: mathematics, statistics, physics, chemistry, finance, computer science, and biology, for instance. This book is an introduction to Monte Carlo methods for anyone who would like to use these methods to study various kinds of mathematical models that arise in diverse areas of application. The book is based on lectures in a graduate course given by the author. It examines theoretical properties of Monte Carlo methods as well as practical issues concerning their computer implementation and statistical analysis. The only formal prerequisite is an undergraduate course in probability. The book is intended to be accessible to students from a wide range of scientific backgrounds. Rather than being a detailed treatise, it covers the key topics of Monte Carlo methods to the depth necessary for a researcher to design, implement, and analyze a full Monte Carlo study of a mathematical or scientific problem. The ideas are illustrated with diverse running examples. There are exercises sprinkled throughout the text. The topics covered include computer generation of random variables, techniques and examples for variance reduction of Monte Carlo estimates, Markov chain Monte Carlo, and statistical analysis of Monte Carlo output.

Rare Event Simulation using Monte Carlo Methods

Gerardo Rubino,Bruno Tuffin
Rare Event Simulation using Monte Carlo Methods Book PDF

Author : Gerardo Rubino,Bruno Tuffin
Publisher : John Wiley & Sons
Page : 278 pages
File Size : 55,9 Mb
Release : 2009-03-18
Category : Mathematics
ISBN : 047074541X

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Rare Event Simulation using Monte Carlo Methods by Gerardo Rubino,Bruno Tuffin Pdf

In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication network of a group of banks, leading to financial losses. Being able to evaluate the probability of rare events is therefore a critical issue. Monte Carlo Methods, the simulation of corresponding models, are used to analyze rare events. This book sets out to present the mathematical tools available for the efficient simulation of rare events. Importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems, typically in computer science or in telecommunications, to chemical reaction analysis in biology or particle transport in physics. Graduate students, researchers and practitioners who wish to learn and apply rare event simulation techniques will find this book beneficial.

Monte Carlo Methods

Malvin H. Kalos,Paula A. Whitlock
Monte Carlo Methods Book PDF

Author : Malvin H. Kalos,Paula A. Whitlock
Publisher : John Wiley & Sons
Page : 217 pages
File Size : 46,5 Mb
Release : 2008-10-20
Category : Science
ISBN : 9783527407606

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Monte Carlo Methods by Malvin H. Kalos,Paula A. Whitlock Pdf

This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.

Uniform Distribution and Quasi-Monte Carlo Methods

Peter Kritzer,Harald Niederreiter,Friedrich Pillichshammer,Arne Winterhof
Uniform Distribution and Quasi Monte Carlo Methods Book PDF

Author : Peter Kritzer,Harald Niederreiter,Friedrich Pillichshammer,Arne Winterhof
Publisher : Walter de Gruyter GmbH & Co KG
Page : 294 pages
File Size : 49,9 Mb
Release : 2014-08-19
Category : Mathematics
ISBN : 9783110375039

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Uniform Distribution and Quasi-Monte Carlo Methods by Peter Kritzer,Harald Niederreiter,Friedrich Pillichshammer,Arne Winterhof Pdf

This book is summarizing the results of the workshop "Uniform Distribution and Quasi-Monte Carlo Methods" of the RICAM Special Semester on "Applications of Algebra and Number Theory" in October 2013. The survey articles in this book focus on number theoretic point constructions, uniform distribution theory, and quasi-Monte Carlo methods. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules enjoy increasing popularity, with many fruitful applications in mathematical practice, as for example in finance, computer graphics, and biology. The goal of this book is to give an overview of recent developments in uniform distribution theory, quasi-Monte Carlo methods, and their applications, presented by leading experts in these vivid fields of research.

Filter Design for Signal Processing Using MATLAB and Mathematica

Miroslav D. Lutovac,Dejan V. Tošić,Brian Lawrence Evans
Filter Design for Signal Processing Using MATLAB and Mathematica Book PDF

Author : Miroslav D. Lutovac,Dejan V. Tošić,Brian Lawrence Evans
Publisher : Miroslav Lutovac
Page : 786 pages
File Size : 55,6 Mb
Release : 2001
Category : Electric filters
ISBN : 9780201361308

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Filter Design for Signal Processing Using MATLAB and Mathematica by Miroslav D. Lutovac,Dejan V. Tošić,Brian Lawrence Evans Pdf

A complete up-to-date reference for advanced analog and digital IIR filter design rooted in elliptic functions. "Revolutionary" in approach, this book opens up completely new vistas in basic analog and digital IIR filter design--regardless of the technology. By introducing exceptionally elegant and creative mathematical stratagems (e.g., accurate replacement of Jacobi elliptic functions by functions comprising polynomials, square roots, and logarithms), optimization routines carried out with symbolic analysis by "Mathematica," and the advance filter design software of MATLAB, it shows readers how to design many types of filters that cannot be designed using conventional techniques. The filter design algorithms can be directly programed in any language or environment such as Visual BASIC, Visual C, Maple, DERIVE, or MathCAD. Signals; Systems; Transforms; Classical Analog Filter Design; Advanced Analog Filter Design Case Studies; Advanced Analog Filter Design Algorithms; Multi-criteria Optimization of Analog Filter Designs; Classical Digital Filter Design; Advanced Digital Filter Design Case Studies; Advanced Digital Filter Design Algorithms; Multi-criteria Optimization of Digital Filter Designs; Elliptic Functions; Elliptic Rational Function.

Random Number Generation and Quasi-Monte Carlo Methods

Harald Niederreiter
Random Number Generation and Quasi Monte Carlo Methods Book PDF

Author : Harald Niederreiter
Publisher : SIAM
Page : 247 pages
File Size : 47,9 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 1611970083

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Random Number Generation and Quasi-Monte Carlo Methods by Harald Niederreiter Pdf

Tremendous progress has taken place in the related areas of uniform pseudorandom number generation and quasi-Monte Carlo methods in the last five years. This volume contains recent important work in these two areas, and stresses the interplay between them. Some developments contained here have never before appeared in book form. Includes the discussion of the integrated treatment of pseudorandom numbers and quasi-Monte Carlo methods; the systematic development of the theory of lattice rules and the theory of nets and (t,s)-sequences; the construction of new and better low-discrepancy point sets and sequences; Nonlinear congruential methods; the initiation of a systematic study of methods for pseudorandom vector generation; and shift-register pseudorandom numbers. Based on a series of 10 lectures presented by the author at a CBMS-NSF Regional Conference at the University of Alaska at Fairbanks in 1990 to a selected group of researchers, this volume includes background material to make the information more accessible to nonspecialists.

Monte Carlo and Quasi-Monte Carlo Sampling

Christiane Lemieux
Monte Carlo and Quasi Monte Carlo Sampling Book PDF

Author : Christiane Lemieux
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 53,9 Mb
Release : 2009-04-03
Category : Mathematics
ISBN : 9780387781655

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Monte Carlo and Quasi-Monte Carlo Sampling by Christiane Lemieux Pdf

Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute. This book presents essential tools for using quasi–Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods—uniform and non-uniform random number generation, variance reduction techniques—but the material is presented to prepare the readers for the next step, which is to replace the random sampling inherent to Monte Carlo by quasi–random sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions, randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book is devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequential Monte Carlo, with a discussion of their quasi–Monte Carlo counterpart. The prerequisites for reading this book are a basic knowledge of statistics and enough mathematical maturity to follow through the various techniques used throughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about Monte Carlo and quasi–Monte Carlo methods and researchers interested in an up-to-date guide to these methods.

Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing

Harald Niederreiter,Peter J. Shiue
Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing Book PDF

Author : Harald Niederreiter,Peter J. Shiue
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461225522

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Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing by Harald Niederreiter,Peter J. Shiue Pdf

Scientists and engineers are increasingly making use of simulation methods to solve problems which are insoluble by analytical techniques. Monte Carlo methods which make use of probabilistic simulations are frequently used in areas such as numerical integration, complex scheduling, queueing networks, and large-dimensional simulations. This collection of papers arises from a conference held at the University of Nevada, Las Vegas, in 1994. The conference brought together researchers across a range of disciplines whose interests include the theory and application of these methods. This volume provides a timely survey of this field and the new directions in which the field is moving.

Sequential Monte Carlo Methods in Practice

Arnaud Doucet,Nando de Freitas,Neil Gordon
Sequential Monte Carlo Methods in Practice Book PDF

Author : Arnaud Doucet,Nando de Freitas,Neil Gordon
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 55,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475734379

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Sequential Monte Carlo Methods in Practice by Arnaud Doucet,Nando de Freitas,Neil Gordon Pdf

Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.