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.
- 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.
- C. de Boor: On calculating with B-splines. J. Approx. Theory 6.1 (1972), pp. 50–62.
- M. G. Cox: The numerical evaluation of B-splines. IMA J. Appl. Math. 10.2 (1972), pp. 134–149.
- 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.
- C. de Boor: A Practical Guide to Splines. Springer, New York (1978).
Textbooks and Recent Surveys
- L. Piegl, W. Tiller: The NURBS Book. 2nd ed. Springer, Berlin (1997).
- K. Höllig: Finite Element Methods with B-Splines. SIAM, Philadelphia (2003).
- K. Höllig, J. Hörner: Approximation and Modeling with B-Splines. SIAM, Philadelphia (2013).
- 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.
- C. de Boor: A comment on Ewald Quak’s “About B-splines”. J. Numer. Anal. Approx. Theory 45.1 (2016), pp. 84–86.
Applications
This content is to be added. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
Own Literature
- J. Valentin: Spline-Approximation unregelmäßig verteilter Daten. Bachelor’s thesis, IMNG, Department of Mathematics, University of Stuttgart, Germany (2012), DOI:
10.18419/opus-5143. - 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. - 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.