Advertisement

Approssimazione di funzioni e di dati

  • Alfio Quarteroni
  • Fausto Saleri
  • Paola Gervasio
Chapter
  • 1.2k Downloads
Part of the UNITEXT book series (UNITEXT, volume 105)

Astratto

In questo capitolo ci interessiamo all’approssimazione polinomiale (globale o locale) di una funzione oppure di una distribuzione di dati. Tratteremo in particolare: i metodi di interpolazione di Lagrange (su nodi equispaziati e di Chebyshev) e di Fourier, l’interpolazione con funzioni spline, il metodo dei minimi quadrati lineari. Il capitolo inizia con vari esempi di interesse applicativo e si conclude con la proposta di numerosi esercizi.

Riferimenti bibliografici

  1. [Atk89]
    Atkinson, K.: An Introduction to Numerical Analysis, 2nd edn. Wiley, New York (1989) zbMATHGoogle Scholar
  2. [BT04]
    Berrut, J.-P., Trefethen, L.-N.: Barycentric Lagrange interpolation. SIAM Rev. 46(3), 501–517 (2004) MathSciNetCrossRefzbMATHGoogle Scholar
  3. [Dav63]
    Davis, P.: Interpolation and Approximation. Blaisdell/Ginn, Toronto/New York (1963) zbMATHGoogle Scholar
  4. [dB01]
    de Boor, C.: A Practical Guide to Splines. Applied Mathematical Sciences. Springer, New York (2001) zbMATHGoogle Scholar
  5. [Die93]
    Dierckx, P.: Curve and Surface Fitting with Splines. Monographs on Numerical Analysis. Clarendon Press/Oxford University Press, New York (1993) zbMATHGoogle Scholar
  6. [DL92]
    DeVore, R., Lucier, B.: Wavelets. Acta Numer. 1992, 1–56 (1992) CrossRefzbMATHGoogle Scholar
  7. [Gau97]
    Gautschi, W.: Numerical Analysis. An Introduction. Birkhäuser Boston, Boston (1997) zbMATHGoogle Scholar
  8. [Hen79]
    Henrici, P.: Barycentric formulas for interpolating trigonometric polynomials and their conjugate. Numer. Math. 33, 225–234 (1979) MathSciNetCrossRefzbMATHGoogle Scholar
  9. [Hes98]
    Hesthaven, J.: From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex. SIAM J. Numer. Anal. 35(2), 655–676 (1998) MathSciNetCrossRefzbMATHGoogle Scholar
  10. [Hig04]
    Higham, N.-J.: The numerical stability of barycentric Lagrange interpolation. IMA J. Numer. Anal. 24(4), 547–556 (2004) MathSciNetCrossRefzbMATHGoogle Scholar
  11. [Mei67]
    Meinardus, G.: Approximation of Functions: Theory and Numerical Methods. Springer Tracts in Natural Philosophy. Springer, New York (1967) CrossRefzbMATHGoogle Scholar
  12. [Nat65]
    Natanson, I.: Constructive Function Theory, vol. III. Interpolation and Approximation Quadratures. Ungar, New York (1965) zbMATHGoogle Scholar
  13. [PBP02]
    Prautzsch, H., Boehm, W., Paluszny, M.: Bezier and B-Spline Techniques. Mathematics and Visualization. Springer, Berlin (2002) CrossRefzbMATHGoogle Scholar
  14. [QSSG14]
    Quarteroni, A., Sacco, R., Saleri, F., Gervasio, P.: Matematica Numerica, 4a edn. Springer, Milano (2014) CrossRefzbMATHGoogle Scholar
  15. [Urb02]
    Urban, K.: Wavelets in Numerical Simulation. Lecture Notes in Computational Science and Engineering. Springer, Berlin (2002) CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Italia Srl. 2017

Authors and Affiliations

  • Alfio Quarteroni
    • 2
    • 1
  • Fausto Saleri
    • 3
  • Paola Gervasio
    • 4
  1. 1.École Polytechnique Fédérale (EPFL)LausanneSwitzerland
  2. 2.Politecnico di MilanoMilanItaly
  3. 3.MOXPolitecnico di MilanoMilanItaly
  4. 4.DICATAMUniversità degli Studi di BresciaBresciaItaly

Personalised recommendations