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Equations --- Matrices --- Algebras, Linear --- Algèbre linéaire --- Numerical solutions --- Solutions numériques --- 519.61 --- 519.61 Numerical methods of algebra --- Numerical methods of algebra

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This book examines the solution of some of the most common problems of numerical computation. By concentrating on one effective algorithm for each basic task, it develops the fundamental theory in a brief, elementary way. There are ample exercises, and codes are provided to reduce the time otherwise required for programming and debugging. Exposes readers to art of numerical computing as well as the science. Readers need only a familiarity with either FORTRAN or C. Applications are taken from a variety of disciplines including engineering, physics, and chemistry.

Numerical analysis --- Analyse numérique --- Data processing --- Informatique --- 519.61 --- -519.62 --- Mathematical analysis --- Numerical methods of algebra --- Numerical methods for solution of ordinary differential equations --- Data processing. --- 519.62 Numerical methods for solution of ordinary differential equations --- 519.61 Numerical methods of algebra --- Analyse numérique --- 519.62 --- Numerical analysis - Data processing

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Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performance on examples and counterexamples which outline their pros and cons. This is done using the MATLABTM software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLABTM computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in engineering, mathematics, physics and computer sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields. In this second edition, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added. From the reviews of the first edition: "This is an excellent and modern textbook in numerical mathematics! It is primarily addressed to undergraduate students in mathematics, physics, computer science and engineering. But you will need a weekly 4 hour lecture for 3 terms lecture to teach all topics treated in this book! Well known methods as well as very new algorithms are given. The methods and their performances are demonstrated by illustrative examples and computer examples. Exercises shall help the reader to understand the theory and to apply it. MATLAB-software satisfies the need of user-friendliness. [....] In the reviewers opinion, the presented book is the best textbook in numerical mathematics edited in the last ten years." Zentralblatt für Mathematik 2001, 991.38387.

Numerical analysis --- 519.61 --- 519.61 Numerical methods of algebra --- Numerical methods of algebra --- Mathematical analysis --- Mathematical Sciences --- Applied Mathematics --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Numerical analysis. --- Applications of Mathematics. --- Mathematics, general. --- Numerical Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- wiskunde --- Mathematics --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Math --- Science --- Numerical analysis - Textbooks --- Analyse numérique. --- Manuels d'enseignement

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Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.

519.61 --- Numerical methods of algebra --- Differential equations, Partial --- Iterative methods (Mathematics) --- Improperly posed problems. --- Iterative methods (Mathematics). --- Differential equations, Partial -- Improperly posed problems. --- Mathematics. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Improperly posed problems --- 519.61 Numerical methods of algebra --- Iteration (Mathematics) --- Improperly posed problems in partial differential equations --- Ill-posed problems --- Inkorrekt gestelltes Problem. --- Regularisierungsverfahren. --- Iteration. --- Nichtlineares inverses Problem. --- Numerical analysis --- Iterative Regularization. --- Nonlinear Ill-Posed Problems. --- Nonlinear Inverse Problems.

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Algebras, Linear --- Numerical calculations --- Numerical calculations. --- Algèbre linéaire --- Calculs numériques --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Calculs numériques --- lineaire algebra --- #TELE:SISTA --- 512.64 --- 519.61 --- 512.64 Linear and multilinear algebra. Matrix theory --- Linear and multilinear algebra. Matrix theory --- Numerical analysis --- Linear algebra --- Mathematical analysis --- Topology --- 519.61 Numerical methods of algebra --- Numerical methods of algebra --- Algebras, Linear. --- Algebra --- Algèbre linéaire