Numerik linearer Gleichungssysteme by Christian Kanzow

By Christian Kanzow

Dieses Buch gibt eine umfassende Darstellung der wichtigsten Verfahren zur numerischen L?sung von linearen Gleichungssystemen. Es ben?tigt zum Verst?ndnis nur sehr geringe mathematische Vorkenntnisse, wie sie meist schon nach einem einsemestrigen Kurs in einem mathematischen oder ingenieurwissenschaftlichen Studiengang vorliegen. Aus diesem Grunde wendet sich das Buch nicht nur an Studierende der Mathematik, Wirtschaftsmathematik oder Technomathematik, sondern auch an den Natur- und Ingenieurwissenschaftler, der in vielen praktischen Anwendungen mit der L?sung von linearen Gleichungssystemen konfrontiert wird.

Inhaltlich besch?ftigt sich das Buch sowohl mit den direkten als auch den iterativen Verfahren. Dabei wird gro?er Wert auf eine sorgf?ltige Herleitung dieser Verfahren gelegt. Ausserdem enth?lt das Buch sehr detaillierte Pseudocodes, mit deren Hilfe sich die jeweiligen Verfahren in einer beliebigen Programmiersprache sofort auf dem laptop realisieren lassen.

Im Einzelnen werden folgende Themenkreise behandelt: Direkte Verfahren f?r lineare Gleichungssysteme, Orthogonalisierungsverfahren f?r lineare Ausgleichsprobleme, Splitting-Methoden, CG-, GMRES- und zahlreiche weitere Krylov-Raum-Methoden, Mehrgitterverfahren.

Show description

Read Online or Download Numerik linearer Gleichungssysteme PDF

Best computational mathematicsematics books

Analytical and numerical approaches to asymptotic problems in analysis: proceedings of the Conference on Analytical and Numerical approaches to Asymptotic Problems, University of Nijmegen, the Netherlands, June 9-13, 1980

A world convention on Analytical and Numerical ways to Asymptotic difficulties was once held within the college of technological know-how, college of Nijmegen, The Netherlands from June ninth via June thirteenth, 1980.

Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis, and Computation (Advances in Design and Control)

This self-contained, functional, entry-level textual content integrates the fundamental rules of utilized arithmetic, utilized chance, and computational technology for a transparent presentation of stochastic strategies and keep watch over for jump-diffusions in non-stop time. the writer covers the $64000 challenge of controlling those platforms and, by utilizing a leap calculus building, discusses the powerful function of discontinuous and nonsmooth homes as opposed to random houses in stochastic structures.

Computational Science – ICCS 2007: 7th International Conference, Beijing, China, May 27 - 30, 2007, Proceedings, Part III

A part of a four-volume set, this publication constitutes the refereed court cases of the seventh foreign convention on Computational technology, ICCS 2007, held in Beijing, China in may perhaps 2007. The papers disguise a wide quantity of issues in computational technological know-how and similar parts, from multiscale physics to instant networks, and from graph idea to instruments for application improvement.

Extra resources for Numerik linearer Gleichungssysteme

Example text

The coefficient of x k , in the polynomial p k (x) of degree < k which agrees with f(x) at x0 , . . , xk. This coefficient depends only on the values of f(x) at the points x0, . . , xk; it is called the kth divided difference of f(x) at the points x0, . . 11) The first divided difference, at any rate, is a ratio of differences. 2-1 Prove that (x - xn). 2-l as 22-2 Calculate the limit of the formula for while all other points remain fixed. 2-3 Prove that the polynomial of degree < n which interpolates f(x) at n + 1 distinct points is f(x) itself in case f(x) is a polynomial of degree < n.

Hence, induction on the number k of zeros may now be used to complete the proof. 36 INTERPOLATION BY POLYNOMIALS Corollary If p(x) and q(x) are two polynomials of degree < k which agree at the k + 1 distinct points z0, . . , zk, then p(x) = q(x) identically. 1, be written in the form with r(x) some polynomial. Suppose that Then some coefficients c0, . . , cm with for which is nonsense. Hence, r(x) = 0 identically, and so p(x) = q(x). ” These considerations concerning zeros of polynomials can be refined through the notion of multiplicity of a zero.

3. 3 Let f(x) be a real-valued function defined on [a, b] and n + 1 times differentiable on (a, b). If p n (x) is the polynomial of degree < n which interpolates f(x) at the n + 1 distinct points there exists x0, . . 18) It is important to note that depends on the point at which the error estimate is required. This dependence need not even be continuous. As we have need in Chap. 16). For, as we show in Sec. 7, f[x0, . . , xn, x] is a well-behaved function of x. 18) to obtain a (usually crude) bound on the error of the interpolating polynomial in that interval.

Download PDF sample

Rated 4.20 of 5 – based on 44 votes