Formulation And Numerical Solution Of Quantum Control Problems

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Formulation and Numerical Solution of Quantum Control Problems

Author : Alfio Borzi
Publisher : SIAM
ISBN 13 : 1611974836
Total Pages : 396 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Formulation and Numerical Solution of Quantum Control Problems by : Alfio Borzi

Download or read book Formulation and Numerical Solution of Quantum Control Problems written by Alfio Borzi and published by SIAM. This book was released on 2017-07-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods. ??

Formulation and Numerical Solution of Quantum Control Problems

Author : Alfio Borzi
Publisher : SIAM
ISBN 13 : 1611974844
Total Pages : 390 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Formulation and Numerical Solution of Quantum Control Problems by : Alfio Borzi

Download or read book Formulation and Numerical Solution of Quantum Control Problems written by Alfio Borzi and published by SIAM. This book was released on 2017-07-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the SchrÓdinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods.

A First Course in Numerical Methods

Author : Uri M. Ascher
Publisher : SIAM
ISBN 13 : 0898719984
Total Pages : 574 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis A First Course in Numerical Methods by : Uri M. Ascher

Download or read book A First Course in Numerical Methods written by Uri M. Ascher and published by SIAM. This book was released on 2011-07-14 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers students a practical knowledge of modern techniques in scientific computing.

Numerical Methods for Conservation Laws

Author : Jan S. Hesthaven
Publisher : SIAM
ISBN 13 : 1611975107
Total Pages : 570 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Numerical Methods for Conservation Laws by : Jan S. Hesthaven

Download or read book Numerical Methods for Conservation Laws written by Jan S. Hesthaven and published by SIAM. This book was released on 2018-01-30 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication.

Computational Uncertainty Quantification for Inverse Problems

Author : Johnathan M. Bardsley
Publisher : SIAM
ISBN 13 : 1611975379
Total Pages : 141 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Computational Uncertainty Quantification for Inverse Problems by : Johnathan M. Bardsley

Download or read book Computational Uncertainty Quantification for Inverse Problems written by Johnathan M. Bardsley and published by SIAM. This book was released on 2018-08-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to both computational inverse problems and uncertainty quantification (UQ) for inverse problems. The book also presents more advanced material on Bayesian methods and UQ, including Markov chain Monte Carlo sampling methods for UQ in inverse problems. Each chapter contains MATLAB? code that implements the algorithms and generates the figures, as well as a large number of exercises accessible to both graduate students and researchers. Computational Uncertainty Quantification for Inverse Problems is intended for graduate students, researchers, and applied scientists. It is appropriate for courses on computational inverse problems, Bayesian methods for inverse problems, and UQ methods for inverse problems.

The Sequential Quadratic Hamiltonian Method

Author : Alfio Borzì
Publisher : CRC Press
ISBN 13 : 1000882470
Total Pages : 391 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis The Sequential Quadratic Hamiltonian Method by : Alfio Borzì

Download or read book The Sequential Quadratic Hamiltonian Method written by Alfio Borzì and published by CRC Press. This book was released on 2023-05-26 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models. It is based on the characterisation of optimal controls in the framework of the Pontryagin maximum principle (PMP). The SQH method is a powerful computational methodology that is capable of development in many directions. The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems discusses its analysis and use in solving nonsmooth ODE control problems, relaxed ODE control problems, stochastic control problems, mixed-integer control problems, PDE control problems, inverse PDE problems, differential Nash game problems, and problems related to residual neural networks. This book may serve as a textbook for undergraduate and graduate students, and as an introduction for researchers in sciences and engineering who intend to further develop the SQH method or wish to use it as a numerical tool for solving challenging optimal control problems and for investigating the Pontryagin maximum principle on new optimisation problems. Features Provides insight into mathematical and computational issues concerning optimal control problems, while discussing many differential models of interest in different disciplines. Suitable for undergraduate and graduate students and as an introduction for researchers in sciences and engineering. Accompanied by codes which allow the reader to apply the SQH method to solve many different optimal control and optimisation problems.

Modelling with Ordinary Differential Equations

Author : Alfio Borzì
Publisher : CRC Press
ISBN 13 : 1351190377
Total Pages : 339 pages
Book Rating : 4.3/5 (511 download)

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Book Synopsis Modelling with Ordinary Differential Equations by : Alfio Borzì

Download or read book Modelling with Ordinary Differential Equations written by Alfio Borzì and published by CRC Press. This book was released on 2020-04-13 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

Interpolatory Methods for Model Reduction

Author : A. C. Antoulas
Publisher : SIAM
ISBN 13 : 1611976081
Total Pages : 244 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Interpolatory Methods for Model Reduction by : A. C. Antoulas

Download or read book Interpolatory Methods for Model Reduction written by A. C. Antoulas and published by SIAM. This book was released on 2020-01-13 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

Methods in Computational Science

Author : Johan Hoffman
Publisher : SIAM
ISBN 13 : 1611976723
Total Pages : 425 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Methods in Computational Science by : Johan Hoffman

Download or read book Methods in Computational Science written by Johan Hoffman and published by SIAM. This book was released on 2021-10-19 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms, with the aim of familiarizing the reader with the field’s theoretical foundations and providing the practical skills to use and develop computational methods. Centered around a set of fundamental algorithms presented in the form of pseudocode, this self-contained textbook extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing. It presents theoretical material alongside several examples and exercises and provides Python implementations of many key algorithms. Methods in Computational Science is for advanced undergraduate and graduate-level students studying computer science and data science. It can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science. It is appropriate for courses in advanced numerical analysis, data science, numerical optimization, and approximation theory.

Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics

Author : Gianluigi Rozza
Publisher : SIAM
ISBN 13 : 1611977258
Total Pages : 501 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics by : Gianluigi Rozza

Download or read book Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics written by Gianluigi Rozza and published by SIAM. This book was released on 2022-11-21 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications. This book will be of interest to researchers and graduate students in the field of reduced order modeling.

An Introduction to Compressed Sensing

Author : M. Vidyasagar
Publisher : SIAM
ISBN 13 : 161197612X
Total Pages : 341 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis An Introduction to Compressed Sensing by : M. Vidyasagar

Download or read book An Introduction to Compressed Sensing written by M. Vidyasagar and published by SIAM. This book was released on 2019-12-03 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing. An Introduction to Compressed Sensing contains substantial material on graph theory and the design of binary measurement matrices, which is missing in recent texts despite being poised to play a key role in the future of compressed sensing theory. It also covers several new developments in the field and is the only book to thoroughly study the problem of matrix recovery. The book supplies relevant results alongside their proofs in a compact and streamlined presentation that is easy to navigate. The core audience for this book is engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing will also find the book of interest.

Vector Extrapolation Methods with Applications

Author : Avram Sidi
Publisher : SIAM
ISBN 13 : 1611974968
Total Pages : 433 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Vector Extrapolation Methods with Applications by : Avram Sidi

Download or read book Vector Extrapolation Methods with Applications written by Avram Sidi and published by SIAM. This book was released on 2017-09-26 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important problem that arises in different disciplines of science and engineering is that of computing limits of sequences of vectors of very large dimension. Such sequences arise, for example, in the numerical solution of systems of linear and nonlinear equations by fixed-point iterative methods, and their limits are simply the required solutions to these systems. The convergence of these sequences, which is very slow in many cases, can be accelerated successfully by using suitable vector extrapolation methods. Vector Extrapolation Methods with Applications is the first book fully dedicated to the subject of vector extrapolation methods. It is a self-contained, up-to-date, and state-of-the-art reference on the theory and practice of the most useful methods. It covers all aspects of the subject, including development of the methods, their convergence study, numerically stable algorithms for their implementation, and their various applications. It also provides complete proofs in most places. As an interesting application, the author shows how these methods give rise to rational approximation procedures for vector-valued functions in the complex plane, a subject of importance in model reduction problems among others. This book is intended for numerical analysts, applied mathematicians, and computational scientists and engineers in fields such as computational fluid dynamics, structures, and mechanical and electrical engineering, to name a few. Since it provides complete proofs in most places, it can also serve as a textbook in courses on acceleration of convergence of iterative vector processes, for example.

Sparse Polynomial Approximation of High-Dimensional Functions

Author : Ben Adcock
Publisher : SIAM
ISBN 13 : 161197688X
Total Pages : 310 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Sparse Polynomial Approximation of High-Dimensional Functions by : Ben Adcock

Download or read book Sparse Polynomial Approximation of High-Dimensional Functions written by Ben Adcock and published by SIAM. This book was released on 2022-02-16 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.

Mathematical Foundations of Finite Elements and Iterative Solvers

Author : SCI085000
Publisher : SIAM
ISBN 13 : 1611977096
Total Pages : 186 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Mathematical Foundations of Finite Elements and Iterative Solvers by : SCI085000

Download or read book Mathematical Foundations of Finite Elements and Iterative Solvers written by SCI085000 and published by SIAM. This book was released on 2022-06-27 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: “This book combines an updated look, at an advanced level, of the mathematical theory of the finite element method (including some important recent developments), and a presentation of many of the standard iterative methods for the numerical solution of the linear system of equations that results from finite element discretization, including saddle point problems arising from mixed finite element approximation. For the reader with some prior background in the subject, this text clarifies the importance of the essential ideas and provides a deeper understanding of how the basic concepts fit together.” — Richard S. Falk, Rutgers University “Students of applied mathematics, engineering, and science will welcome this insightful and carefully crafted introduction to the mathematics of finite elements and to algorithms for iterative solvers. Concise, descriptive, and entertaining, the text covers all of the key mathematical ideas and concepts dealing with finite element approximations of problems in mechanics and physics governed by partial differential equations while interweaving basic concepts on Sobolev spaces and basic theorems of functional analysis presented in an effective tutorial style.” — J. Tinsley Oden, The University of Texas at Austin This textbook describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. Reflecting the author’s decade of experience in the field, Mathematical Foundations of Finite Elements and Iterative Solvers examines the crucial interplay between analysis, discretization, and computations in modern numerical analysis; furthermore, it recounts historical developments leading to current state-of-the-art techniques. While self-contained, this textbook provides a clear and in-depth discussion of several topics, including elliptic problems, continuous Galerkin methods, iterative solvers, advection-diffusion problems, and saddle point problems. Accessible to readers with a beginning background in functional analysis and linear algebra, this text can be used in graduate-level courses on advanced numerical analysis, data science, numerical optimization, and approximation theory. Professionals in numerical analysis and finite element methods will also find the book of interest.

Basics and Trends in Sensitivity Analysis: Theory and Practice in R

Author : Sébastien Da Veiga
Publisher : SIAM
ISBN 13 : 1611976693
Total Pages : 307 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Basics and Trends in Sensitivity Analysis: Theory and Practice in R by : Sébastien Da Veiga

Download or read book Basics and Trends in Sensitivity Analysis: Theory and Practice in R written by Sébastien Da Veiga and published by SIAM. This book was released on 2021-10-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. The authors use a practical point of view and real case studies as well as numerous examples, and applications of the different approaches are illustrated throughout using R code to explain their usage and usefulness in practice. Basics and Trends in Sensitivity Analysis: Theory and Practice in R covers a lot of material, including theoretical aspects of Sobol’ indices as well as sampling-based formulas, spectral methods, and metamodel-based approaches for estimation purposes; screening techniques devoted to identifying influential and noninfluential inputs; variance-based measures when model inputs are statistically dependent (and several other approaches that go beyond variance-based sensitivity measures); and a case study in R related to a COVID-19 epidemic model where the full workflow of sensitivity analysis combining several techniques is presented. This book is intended for engineers, researchers, and undergraduate students who use complex numerical models and have an interest in sensitivity analysis techniques and is appropriate for anyone with a solid mathematical background in basic statistical and probability theories who develops and uses numerical models in all scientific and engineering domains.

Mathematical Theory of Finite Elements

Author : Leszek F. Demkowicz
Publisher : SIAM
ISBN 13 : 1611977738
Total Pages : 217 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Mathematical Theory of Finite Elements by : Leszek F. Demkowicz

Download or read book Mathematical Theory of Finite Elements written by Leszek F. Demkowicz and published by SIAM. This book was released on 2023-09-22 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed.. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin’s theory, followed by the Lax–Milgram theorem and Cea’s lemma to the Babuska theorem and Brezzi’s theory. He finishes with an introduction to the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. Based on the author’s personal lecture notes for a popular version of his graduate course on mathematical theory of finite elements, the book includes a unique exposition of the concept of discrete stability and the means to guarantee it, a coherent presentation of finite elements forming the exact grad-curl-div sequence, and an introduction to the DPG method. Intended for graduate students in computational science, engineering, and mathematics programs, Mathematical Theory of Finite Elements is also appropriate for graduate mathematics and mathematically oriented engineering students. Instructors will find the book useful for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.

Computational Optimization of Systems Governed by Partial Differential Equations

Author : Alfio Borzi
Publisher : SIAM
ISBN 13 : 1611972043
Total Pages : 295 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Computational Optimization of Systems Governed by Partial Differential Equations by : Alfio Borzi

Download or read book Computational Optimization of Systems Governed by Partial Differential Equations written by Alfio Borzi and published by SIAM. This book was released on 2012-01-26 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a bridge between continuous optimization and PDE modelling and focuses on the numerical solution of the corresponding problems. Intended for graduate students in PDE-constrained optimization, it is also suitable as an introduction for researchers in scientific computing or optimization.