Stochastic Methods In Scientific Computing

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Stochastic Methods in Scientific Computing

Kurt Langfeld,Massimo D'Elia,Biagio Lucini
Stochastic Methods in Scientific Computing Book PDF

Author : Kurt Langfeld,Massimo D'Elia,Biagio Lucini
Publisher : C&h/CRC Press
Page : 0 pages
File Size : 49,9 Mb
Release : 2024
Category : Computers
ISBN : 1032775599

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Stochastic Methods in Scientific Computing by Kurt Langfeld,Massimo D'Elia,Biagio Lucini Pdf

"Stochastic Methods in Scientific Computing: From Foundations to Advanced Techniques introduces the reader to advanced concepts in stochastic modelling, rooted in an intuitive yet rigorous presentation of the underlying mathematical concepts. A particular emphasis is placed on illuminating the underpinning Mathematics, and yet have the practical applications in mind. The reader will find valuable insights into topics ranging from Social Sciences and Particle Physics to modern-day Computer Science with Machine Learning and AI in focus. The book also covers recent specialised techniques for notorious issues in the field of stochastic simulations, providing a valuable reference for advanced readers with an active interest in the field"--

Stochastic Methods in Scientific Computing

Massimo D'Elia,Kurt Langfeld,Biagio Lucini
Stochastic Methods in Scientific Computing Book PDF

Author : Massimo D'Elia,Kurt Langfeld,Biagio Lucini
Publisher : CRC Press
Page : 661 pages
File Size : 53,6 Mb
Release : 2024-06-11
Category : Mathematics
ISBN : 9781351652223

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Stochastic Methods in Scientific Computing by Massimo D'Elia,Kurt Langfeld,Biagio Lucini Pdf

Stochastic Methods in Scientific Computing: From Foundations to Advanced Techniques introduces the reader to advanced concepts in stochastic modelling, rooted in an intuitive yet rigorous presentation of the underlying mathematical concepts. A particular emphasis is placed on illuminating the underpinning Mathematics, and yet have the practical applications in mind. The reader will find valuable insights into topics ranging from Social Sciences and Particle Physics to modern-day Computer Science with Machine Learning and AI in focus. The book also covers recent specialised techniques for notorious issues in the field of stochastic simulations, providing a valuable reference for advanced readers with an active interest in the field. Features Self-contained, starting from the theoretical foundations and advancing to the most recent developments in the field Suitable as a reference for post-graduates and researchers or as supplementary reading for courses in numerical methods, scientific computing, and beyond Interdisciplinary, laying a solid ground for field-specific applications in finance, physics and biosciences on common theoretical foundations Replete with practical examples of applications to classic and current research problems in various fields.

Stochastic Optimization

Johannes Schneider,Scott Kirkpatrick
Stochastic Optimization Book PDF

Author : Johannes Schneider,Scott Kirkpatrick
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 52,5 Mb
Release : 2007-08-06
Category : Computers
ISBN : 9783540345602

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Stochastic Optimization by Johannes Schneider,Scott Kirkpatrick Pdf

This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.

Fundamentals of Scientific Computing

Bertil Gustafsson
Fundamentals of Scientific Computing Book PDF

Author : Bertil Gustafsson
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 50,7 Mb
Release : 2011-06-11
Category : Mathematics
ISBN : 9783642194955

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Fundamentals of Scientific Computing by Bertil Gustafsson Pdf

The book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built? The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation. This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.

Stochastic Numerics for Mathematical Physics

Grigori N. Milstein,Michael V. Tretyakov
Stochastic Numerics for Mathematical Physics Book PDF

Author : Grigori N. Milstein,Michael V. Tretyakov
Publisher : Springer Nature
Page : 754 pages
File Size : 46,7 Mb
Release : 2021-12-03
Category : Computers
ISBN : 9783030820404

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Stochastic Numerics for Mathematical Physics by Grigori N. Milstein,Michael V. Tretyakov Pdf

This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

Numerical Methods for Stochastic Computations

Dongbin Xiu
Numerical Methods for Stochastic Computations Book PDF

Author : Dongbin Xiu
Publisher : Princeton University Press
Page : 142 pages
File Size : 41,9 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781400835348

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Numerical Methods for Stochastic Computations by Dongbin Xiu Pdf

The@ first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC methods through numerical examples and rigorous development; details the procedure for converting stochastic equations into deterministic ones; using both the Galerkin and collocation approaches; and discusses the distinct differences and challenges arising from high-dimensional problems. The last section is devoted to the application of gPC methods to critical areas such as inverse problems and data assimilation. Ideal for use by graduate students and researchers both in the classroom and for self-study, Numerical Methods for Stochastic Computations provides the required tools for in-depth research related to stochastic computations. The first graduate-level textbook to focus on the fundamentals of numerical methods for stochastic computations Ideal introduction for graduate courses or self-study Fast, efficient, and accurate numerical methods Polynomial approximation theory and probability theory included Basic gPC methods illustrated through examples

Large Scale Scientific Computing

Deuflhard
Large Scale Scientific Computing Book PDF

Author : Deuflhard
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468467543

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Large Scale Scientific Computing by Deuflhard Pdf

In this book, the new and rapidly expanding field of scientific computing is understood in a double sense: as computing for scientific and engineering problems and as the science of doing such computations. Thus scientific computing touches at one side mathematical modelling (in the various fields of applications) and at the other side computer science. As soon as the mathematical models de scribe the features of real life processes in sufficient detail, the associated computations tend to be large scale. As a consequence, interest more and more focusses on such numerical methods that can be expected to cope with large scale computational problems. Moreover, given the algorithms which are known to be efficient on a tradi tional computer, the question of implementation on modern supercomputers may get crucial. The present book is the proceedings of a meeting on "Large Scale Scientific Computing" , that was held a t the Oberwolfach Mathematical Institute (July 14-19, 1985) under the auspices of the Sonderforschungsbereich 123 of the University of Heidelberg. Participants included applied scientists with computational interests, numerical analysts, and experts on modern parallel computers. 'l'he purpose of the meeting was to establish a common under standing of recent issues in scientific computing, especially in view of large scale problems. Fields of applications, which have been covered, included semi-conductor design, chemical combustion, flow through porous media, climatology, seismology, fluid dynami. cs, tomography, rheology, hydro power plant optimization, subwil. y control, space technology.

Random Differential Equations in Scientific Computing

Tobias Neckel,Florian Rupp
Random Differential Equations in Scientific Computing Book PDF

Author : Tobias Neckel,Florian Rupp
Publisher : Walter de Gruyter
Page : 650 pages
File Size : 43,6 Mb
Release : 2013-12-17
Category : Mathematics
ISBN : 9788376560267

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Random Differential Equations in Scientific Computing by Tobias Neckel,Florian Rupp Pdf

This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.

Numerical and Symbolic Scientific Computing

Ulrich Langer,Peter Paule
Numerical and Symbolic Scientific Computing Book PDF

Author : Ulrich Langer,Peter Paule
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 53,9 Mb
Release : 2011-11-19
Category : Mathematics
ISBN : 9783709107942

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Numerical and Symbolic Scientific Computing by Ulrich Langer,Peter Paule Pdf

The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.

Scientific Computing

Michael T. Heath
Scientific Computing Book PDF

Author : Michael T. Heath
Publisher : SIAM
Page : 567 pages
File Size : 45,9 Mb
Release : 2018-11-14
Category : Mathematics
ISBN : 9781611975581

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Scientific Computing by Michael T. Heath Pdf

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results. In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.

Constructive Computation in Stochastic Models with Applications

Quan-Lin Li
Constructive Computation in Stochastic Models with Applications Book PDF

Author : Quan-Lin Li
Publisher : Springer Science & Business Media
Page : 693 pages
File Size : 44,6 Mb
Release : 2011-02-02
Category : Mathematics
ISBN : 9783642114922

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Constructive Computation in Stochastic Models with Applications by Quan-Lin Li Pdf

"Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable. Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.

Stochastic Methods for Modeling and Predicting Complex Dynamical Systems

Nan Chen
Stochastic Methods for Modeling and Predicting Complex Dynamical Systems Book PDF

Author : Nan Chen
Publisher : Springer Nature
Page : 208 pages
File Size : 40,9 Mb
Release : 2023-03-13
Category : Mathematics
ISBN : 9783031222498

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Stochastic Methods for Modeling and Predicting Complex Dynamical Systems by Nan Chen Pdf

This book enables readers to understand, model, and predict complex dynamical systems using new methods with stochastic tools. The author presents a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. An emphasis is placed on the balance between computational efficiency and modeling accuracy, providing readers with ideas to build useful models in practice. Successful modeling of complex systems requires a comprehensive use of qualitative and quantitative modeling approaches, novel efficient computational methods, physical intuitions and thinking, as well as rigorous mathematical theories. As such, mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools are presented. Both theoretical and numerical approaches are included, allowing readers to choose suitable methods in different practical situations. The author provides practical examples and motivations when introducing various mathematical and stochastic tools and merges mathematics, statistics, information theory, computational science, and data science. In addition, the author discusses how to choose and apply suitable mathematical tools to several disciplines including pure and applied mathematics, physics, engineering, neural science, material science, climate and atmosphere, ocean science, and many others. Readers will not only learn detailed techniques for stochastic modeling and prediction, but will develop their intuition as well. Important topics in modeling and prediction including extreme events, high-dimensional systems, and multiscale features are discussed.

Stochastic Systems

Adomian
Stochastic Systems Book PDF

Author : Adomian
Publisher : Academic Press
Page : 352 pages
File Size : 50,8 Mb
Release : 1983-07-29
Category : Computers
ISBN : 9780080956756

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Stochastic Systems by Adomian Pdf

Stochastic Systems

An Introduction to Computational Stochastic PDEs

Gabriel J. Lord,Catherine E. Powell,Tony Shardlow
An Introduction to Computational Stochastic PDEs Book PDF

Author : Gabriel J. Lord,Catherine E. Powell,Tony Shardlow
Publisher : Cambridge University Press
Page : 516 pages
File Size : 52,8 Mb
Release : 2014-08-11
Category : Business & Economics
ISBN : 9780521899901

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An Introduction to Computational Stochastic PDEs by Gabriel J. Lord,Catherine E. Powell,Tony Shardlow Pdf

This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.

Applied Scientific Computing

Peter R. Turner,Thomas Arildsen,Kathleen Kavanagh
Applied Scientific Computing Book PDF

Author : Peter R. Turner,Thomas Arildsen,Kathleen Kavanagh
Publisher : Springer
Page : 272 pages
File Size : 48,7 Mb
Release : 2018-07-18
Category : Computers
ISBN : 9783319895758

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Applied Scientific Computing by Peter R. Turner,Thomas Arildsen,Kathleen Kavanagh Pdf

This easy-to-understand textbook presents a modern approach to learning numerical methods (or scientific computing), with a unique focus on the modeling and applications of the mathematical content. Emphasis is placed on the need for, and methods of, scientific computing for a range of different types of problems, supplying the evidence and justification to motivate the reader. Practical guidance on coding the methods is also provided, through simple-to-follow examples using Python. Topics and features: provides an accessible and applications-oriented approach, supported by working Python code for many of the methods; encourages both problem- and project-based learning through extensive examples, exercises, and projects drawn from practical applications; introduces the main concepts in modeling, python programming, number representation, and errors; explains the essential details of numerical calculus, linear, and nonlinear equations, including the multivariable Newton method; discusses interpolation and the numerical solution of differential equations, covering polynomial interpolation, splines, and the Euler, Runge–Kutta, and shooting methods; presents largely self-contained chapters, arranged in a logical order suitable for an introductory course on scientific computing. Undergraduate students embarking on a first course on numerical methods or scientific computing will find this textbook to be an invaluable guide to the field, and to the application of these methods across such varied disciplines as computer science, engineering, mathematics, economics, the physical sciences, and social science.