Least squares splines with free knots: Global optimization approach

Applied Mathematics and Computation

Volumn 149, Issue 3, 2004, Pages 783-798

  Beliakov, Gleb ^a  

^a DEAKIN UNIVERSITY   (Australia)

Author keywords

Cutting angle method; Global optimisation; Least squares splines; Regression splines; Splines with free knots

Indexed keywords

COMPUTATIONAL COMPLEXITY; GENETIC ALGORITHMS; GLOBAL OPTIMIZATION; LEAST SQUARES APPROXIMATIONS; LINEAR SYSTEMS; MATHEMATICAL TRANSFORMATIONS; PERSONAL COMPUTERS; PROBLEM SOLVING; RANDOM PROCESSES; SIMULATED ANNEALING;

CUTTING ANGLE METHOD; LEAST SQUARE SPLINES; REGRESSION SPLINES;

SPLINES;

EID: 0347758639     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(03)00179-6     Document Type: Article

References (24)

1. Andramonov M., Rubinov A., Glover B. Cutting angle method in global optimization. Appl. Math. Lett. 12:1999;95-100.
2. Bagirov A., Rubinov A. Global minimization of increasing positively homogeneous function over the unit simplex. Ann. Oper. Res. 98:2000;171-187.
3. Bagirov A., Rubinov A. Modified versions of the cutting angle method. Hadjisavvas N., Pardalos P.M. Convex Analysis and Global Optimization. 2001;Kluwer, Dordrecht.
4. Bagirov A. Derivative-free methods for unconstrained nonsmooth optimization and its numerical analysis. J. Invest. Oper. 19:1999;75-93.
5. Batten L.M., Beliakov G. Fast algorithm for the cutting angle method of global optimization. J. Global Optim. 25:2002;149-161.
6. Beliakov G. Shape preserving approximation using least squares splines. Approx. Theory Appl. 16:2000;80-98.
7. de Boor C. A Practical Guide to Splines. 1978;Springer, New York, Heidelberg.
8. Dierckx P. Curve and Surface Fitting with Splines. 1995;Clarendon Press, Oxford.
9. Horst R., Pardalos P., Thoai N. Introduction to Global Optimization. 1995;Kluwer, Dordrecht.
10. Hu Y. An algorithm for data reduction using splines with free knots. IMA J. Numer. Anal. 13:1993;365-381.
11. Jupp D. Approximation to data by splines with free knots. SIAM J. Numer. Anal. 15:1978;328-343.
12. Lanshammar H. On practical evaluation of differentiation techniques for human gait analysis. J. Biomech. 5:1982;99-105.
13. Loach P.D., Wathen A.J. On the best least squares approximation of continuous functions using linear splines with free knots. IMA J. Numer. Anal. 11:1991;393-409.
14. Lyche T., Morken K. A data reduction strategy for splines with applications to the approximation of functions and data. IMA J. Numer. Anal. 8:1988;185-208.
15. Lyche T., Morken K. The sensitivity of a spline function to perturbations of the knots. BIT. 39:1999;305-322.
16. Meinardus G., Nurnberger G., Sommer M., Strauss H. Algorithms for piecewise polynomials and splines with free knots. Math. Comp. 53:1989;235-247.
17. Mladineo R. An algorithm for finding the global maximum of a multimodal, multivariate function. Math. Progr. 34:1986;188-200.
18. Pallachke D., Rolewicz S. Foundations of Mathematical Optimization (Convex Analysis with Linearity). 1997;Kluwer, Dordrecht.
19. Rubinov A. Abstract Convexity and Global Optimization. 2000;Kluwer, Dordrecht.
20. Rubinov A., Andramonov M. Lipschitz programming via increasing convex-along-rays functions. Optim. Meth. Software. 10:1999;763-781.
21. Schumaker L., Stanley S. Shape-preserving knot removal. Comp. Aided Geom. Des. 13:1996;851-872.
22. Schutze T., Schwetlick H. Constrained approximation by splines with free knots. BIT. 37:1997;105-137.
23. Schwetlick H., Schutze T. Least squares approximation by splines with free knots. BIT. 35:1995;361-384.
24. Torn A., Zilinskas A. Global Optimization. 1989;Springer, Heidelberg.