e-book A Brief Introduction to Numerical Analysis

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Roots of polynomials. Roots of polynomials: the companion matrix. Video 7 videos.

Bibliographic Information

Large-scale systems of linear equations. Simple iteration for a linear system. Jacobi iteration. Convergence criteria for simple iteration. Seidel's iteration.

Successive over-relaxation. Canonic form of two-step iterative methods for linear systems. Variational approaches: minimum residual method. Show More. Video 9 videos. Interpolation and approximation. Modelling of data. Linear least squares problem. Ordinary least squares: the normal equations.


Ordinary least squares: QR decomposition of the design matrix. Global polynomial interpolation. Lagrange interpolating polynomial. Quantifying interpolation errors. Runge phenomenon. Chebyshev nodes. Interpolation of the Runge function. Video 13 videos.


ISBN 13: 9781461264132

Numerical derivatives. Numerical derivatives: finite differences. Truncation and roundoff errors: an interplay. Higher order schemes. Richardson extrapolation. Integration: numeric quadratures. Convergence rates of simple quadratures. Simple geometric quadratures: Trapezoids, Simpson's rule and all that. Error bounds for quadratures.

Instruction Type(s)

Romberg extrapolation. Integrals with singularities. A check of convergence. Recap: Newton-Cotes vs Gaussian quadratures. Gaussian quadratures. Initial value problem for an ODE. Approximation and convergence. Truncation error or Euler-like schemes. Awrejcewicz, J. Mrozowski, S.

Zagrodny, S. Banasiak and L. By Lianggang Guo and He Yang. Jurado-Navas, J. Garrido-Balsells and A. Roth, D.

A Brief Introduction to Numerical Analysis | Eugene E. Tyrtyshnikov | Springer

Chamoret, J. Badin, JR. Imbert and S. By Takafumi Suzuki and Masaki Takahashi.

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  • An Introduction to Numerical Methods and Analysis, 2nd Edition?

By Qingzhi Yan and Xiangzhen Yan. By Seiya Ueno and Takehiro Higuchi. This is made possible by the EU reverse charge method. Edited by Jan Awrejcewicz. Would you like to change to the United States site? James F. The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications.

The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features:.