Literature About B-Splines

This page lists the references for the website, as well as useful literature, split into categories. Within each category, the references are sorted in chronological order.


Original Papers by de Boor et al.

  • [sta_anchor id=”Schoenberg46Contributions”]I. J. Schoenberg: Contributions to the problem of approximation of equidistant data by analytic functions. Quart. Appl. Math. 4 (1946), pp. 45–99, 112–141.
  • [sta_anchor id=”Boor72Calculating”]C. de Boor: On calculating with B-splines. J. Approx. Theory 6.1 (1972), pp. 50–62.
  • [sta_anchor id=”Cox72Numerical”]M. G. Cox: The numerical evaluation of B-splines. IMA J. Appl. Math. 10.2 (1972), pp. 134–149.
  • [sta_anchor id=”Boor76Splines”]C. de Boor: Splines as linear combinations of B-splines. A survey. In G. G. Lorentz, C. K. Chui, L. L. Schumaker (eds.): Approximation Theory II. Academic Press, New York (1976), pp. 1–47.
  • [sta_anchor id=”Boor78Splines”]C. de Boor: A Practical Guide to Splines. Springer, New York (1978).

Textbooks and Recent Surveys

  • [sta_anchor id=”Piegl97NURBS”]L. Piegl, W. Tiller: The NURBS Book. 2nd ed. Springer, Berlin (1997).
  • [sta_anchor id=”Hoellig03Finite”]K. Höllig: Finite Element Methods with B-Splines. SIAM, Philadelphia (2003).
  • [sta_anchor id=”Hoellig13Approximation”]K. Höllig, J. Hörner: Approximation and Modeling with B-Splines. SIAM, Philadelphia (2013).
  • [sta_anchor id=”Quak16About”]E. Quak: About B-splines. Twenty answers to one question: What is the cubic B-spline for the knots \(-2, -1, 0, 1, 2\)? J. Numer. Anal. Approx. Theory 45.1 (2016), pp. 37–83.
  • [sta_anchor id=”Boor16Comment”]C. de Boor: A comment on Ewald Quak’s “About B-splines”. J. Numer. Anal. Approx. Theory 45.1 (2016), pp. 84–86.

Applications

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Own Literature

  • [sta_anchor id=”Valentin12Spline”]J. Valentin: Spline-Approximation unregelmäßig verteilter Daten. Bachelor’s thesis, IMNG, Department of Mathematics, University of Stuttgart, Germany (2012), DOI: 10.18419/opus-5143.
  • [sta_anchor id=”Valentin14Hierarchische”]J. Valentin: Hierarchische Optimierung mit Gradientenverfahren auf Dünngitterfunktionen. Master’s thesis, IPVS, Department of Computer Science, University of Stuttgart, Germany (2014), DOI: 10.18419/opus-3462.
  • [sta_anchor id=”Valentin16Hierarchical”]J. Valentin, D. Pflüger: Hierarchical Gradient-Based Optimization with B-Splines on Sparse Grids. In J. Garcke, D. Pflüger (eds.): Sparse Grids and Applications – Stuttgart 2014, Springer, Heidelberg (2016), pp. 315–336, DOI: 10.1007/978-3-319-28262-6_13.