Aronsson, Gunnar Perfect splines and nonlinear optimal control theory. (English) Zbl 0408.41005 J. Approximation Theory 25, 142-152 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 3 Documents MSC: 41A15 Spline approximation 49K15 Optimality conditions for problems involving ordinary differential equations Keywords:Perfect Splines; Nonlinear Optimal Minimum; Discontinuous Piece-Wise Coninuity; Boundary Conditions; Nonlinear Optimal Control Theory PDFBibTeX XMLCite \textit{G. Aronsson}, J. Approx. Theory 25, 142--152 (1979; Zbl 0408.41005) Full Text: DOI References: [1] Aronsson, G., Minimization problems for the functional \(supxF(x, ƒ(x), ƒ′(x)), I\), Ark. Mat., 6, 33-53 (1965) · Zbl 0156.12502 [2] Aronsson, G., Minimization problems for the functional \(supxF(x, ƒ(x), ƒ′(x))\), II, Ark. Mat., 6, 409-431 (1966) · Zbl 0156.12502 [3] Aronsson, G., Minimization problems for the functional \(supxF(x, ƒ(x), ƒ′(x))\), III, Ark. Mat., 7, 509-512 (1968) · Zbl 0181.11902 [4] Aronsson, G., Pontryagin’s maximum principle and a minimax problem, Math. Scand., 29, 55-71 (1971) · Zbl 0236.49014 [5] Carter, D. S., A minimum-maximum problem for differential expressions, Canad. J. Math., 9, 132-140 (1957) · Zbl 0077.29001 [6] Coppel, W. A., Disconjugacy, (Lecture Notes in Mathematics, No. 220 (1971), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0224.34003 [7] Fisher, S. D., Solutions of some non-linear variational problems in \(L^∞\) and the problem of minimum curvature, Arch. Rational Mech. Anal., 61, 291-305 (1976) · Zbl 0329.49010 [8] Fisher, S. D.; Jerome, J. W., Perfect spline solutions to \(L^∞\) extremal problems, J. Approximation Theory, 12, 78-90 (1974) · Zbl 0292.49021 [9] Fisher, S. D.; Jerome, J. W., The existence, characterization and essential uniqueness of solutions to \(L^∞\) extremal problems, Trans. Amer. Math. Soc., 187, 391-404 (1974) · Zbl 0289.49008 [10] Fisher, S. D.; Jerome, J. W., Minimum Norm Extremals in Function Spaces, (Lecture Notes in Mathematics No. 479 (1975), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0345.49003 [11] Glaeser, G., Prolongement Extremal de Fonctions Differentiables, (Publications de la section de Mathématique de la Faculté des Sciences de Rennes (1967), Université de Rennes: Université de Rennes France) · Zbl 0259.41011 [12] Hale, J. K., Ordinary Differential Equations (1969), Wiley: Wiley New York · Zbl 0186.40901 [13] Hartman, P., On disconjugacy criteria, (Proc. Amer. Math. Soc., 24 (1970)), 374-381 · Zbl 0191.38301 [14] Karlin, S., Some variational problems on certain Sobolev spaces and perfect splines, Bull. Amer. Math. Soc., 79, 124-128 (1973) · Zbl 0253.41010 [15] Lee, E. B.; Markus, L., Foundations of Optimal Control Theory (1967), Wiley: Wiley New York · Zbl 0159.13201 [16] Mangasarian, O. L.; Schumaker, L. L., Splines via optimal control, (Schoenberg, I. J., Approximations with Special Emphasis on Spline Functions (1969), Academic Press: Academic Press New York) · Zbl 0268.49026 [17] McClure, D. E., Perfect spline solutions of \(L^∞\) extremal problems by control methods, J. Approximation Theory, 15, 226-242 (1975) · Zbl 0314.41006 [18] Pontryagin, L. S.; Boltyanskii, V. G.; Gamkrelidze, R. V.; Mishchenko, E. F., The Mathematical Theory of Optimal Processes (1962), Wiley: Wiley New York · Zbl 0102.32001 [19] Reid, W. T., Ordinary linear differential operators of minimum norm, Duke Math. J., 29, 591-606 (1962) · Zbl 0171.35001 [20] Schoenberg, I. J., The perfect \(B\)-splines and a time optimal control problem, Israel J. Math., 10, 275-291 (1971) · Zbl 0273.41006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.