Numerische Mathematik für Informatiker
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Numerische Mathematik für Informatiker: (Springer-Lehrbuch)

Numerische Mathematik für Informatiker: (Springer-Lehrbuch)


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Table of Contents:
1 Fehleranalyse.- 1.1 Einleitung.- 1.2 Fehler.- 1.3 Fehlerfortpflanzung und Stabilität.- 1.4 Rundungsfehler bei Gleitkomma-Arithmetik.- 2 Polynome und rationale Funktionen.- 2.1 Einleitung.- 2.2 Polynome.- 2.3 ?ebyšev-Polynome.- 2.4 Polynomauswertung.- 2.5 Rationale Funktionen.- 2.6 Numerische Stabilität von arithmetischen Ausdrücken.- 2.7 Lineare Rekursionen.- 3 Interpolation und Quadratur.- 3.1 Einleitung.- 3.2 Algebraische Interpolation.- 3.3 Die Newton-Darstellung des Interpolationspolynoms.- 3.4 Integraldarstellung dividierter Differenzen und B-Splines.- 3.5 Interpolationsfehler.- 3.6 Quadratur mit Hilfe von Interpolation.- 3.7 Quadraturfehler.- 3.8 Gauß-Quadraturformeln.- 4 Splines und Graphik.- 4.1 Einleitung.- 4.2 Mathematische Filter.- 4.3 Bernstein-Polynome.- 4.4 Die Bézier-Darstellung eines Polynoms.- 4.5 Stückweise polynomiale Funktionen.- 4.6 Spline-Funktionen.- 4.7 Kubische B-Splines.- 4.8 Die Minimalkrümmungseigenschaft.- 4.9 Kubische Spline-Kurven und das Prinzip eines Zeichengenerators.- 4.10 Tensorierung und kubische Spline-Flächen.- 5 Periodizität und schnelle Fourier-Transformation.- 5.1 Einleitung.- 5.2 Exponentialfunktion und trigonometrische Funktionen.- 5.3 Die N-ten Einheitswurzeln.- 5.4 Trigonometrische Interpolation.- 5.5 Der diskrete Fourier-Operator.- 5.6 Der FFT-Algorithmus.- 5.7 Schnelle Multiplikation großer Zahlen.- 6 Approximationsverfahren.- 6.1 Einleitung.- 6.2 Normierte Vektorräume.- 6.3 Existenz von Bestapproximationen.- 6.4 Skalarprodukte und unitäre Vektorräume.- 6.5 Approximation in unitären Vektorräumen.- 6.6 Fourier-?ebyšev-Entwicklung stetiger Funktionen.- 6.7 Das Prinzip einer Log-Routine.- 7 Elimination und lineare Gleichungssysteme.- 7.1 Einleitung.- 7.2 Elementare Matrizen und Gleichungssysteme.- 7.3 DasGaußsche Eliminationsverfahren.- 7.4 Das Cholesky-Verfahren.- 7.5 Schnelle Matrix-Algorithmen.- 7.6 Ausgleichsrechnung.- 8 Schwach besetzte Matrizen und Graphen.- 8.1 Einleitung.- 8.2 Speicherungstechniken für schwach besetzte Matrizen.- 8.3 Graphen.- 8.4 Sortierung mit dem Cuthill-McKee-Algorithmus.- 8.5 Symbolische und numerische Cholesky-Faktorisierung.- 8.6 Schwach besetzte Least-squares-Probleme.- 9 Iteration und nichtlineare Gleichungen.- 9.1 Einleitung.- 9.2 Die Parabeliteration.- 9.3 Der Banachsche Fixpunktsatz.- 9.4 Lösung von nichtlinearen Gleichungen.- 9.5 Iterative Lösung von linearen Gleichungssystemen.- 9.6 Das Prinzip einer Quadratwurzel-Routine.- Lösungshinweise.- Literatur.- Symbolverzeichnis.


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Product Details
  • ISBN-13: 9783540567844
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Edition: Revised edition
  • Language: German
  • Returnable: N
  • Series Title: Springer-Lehrbuch
  • ISBN-10: 3540567844
  • Publisher Date: 17 Aug 1993
  • Binding: Paperback
  • Height: 235 mm
  • No of Pages: 406
  • Returnable: N
  • Width: 155 mm


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Numerische Mathematik für Informatiker: (Springer-Lehrbuch)
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