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Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.
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Excellent advanced-undergraduate and graduate text covers norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation and more. Careful analysis and stress on techniques for developing new methods. Examples and problems. 1966 edition. Bibliography.
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This textbook is written primarily for undergraduate mathematicians and also appeals to students working at an advanced level in other disciplines. The text begins with a clear motivation for the study of numerical analysis based on real-world problems. The authors then develop the necessary machinery including iteration, interpolation, boundary-value problems and finite elements. Throughout, the authors keep an eye on the analytical basis for the work and add historical notes on the development of the subject. There are numerous exercises for students.
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An accessible yet rigorous mathematical introduction, A Theoretical Introduction to Numerical Analysis provides a pedagogical account of the fundamentals of numerical analysis. Using numerical methods from real analysis, linear algebra, and differential equations, the authors explain basic concepts, such as error, discretization, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the smoothness of approximated functions in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation.
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