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A dual basis for L-splines and applications. (English) Zbl 0463.41008


MSC:

41A15 Spline approximation
41A05 Interpolation in approximation theory

Citations:

Zbl 0343.41011
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Full Text: DOI

References:

[1] de Boor, C., Splines as linear combinations of \(B\)-splines. A survey, (Lorentz, G. G.; Chui, C. K.; Schumaker, L. L., Approximation Theory II (1976), Academic Press: Academic Press New York), 1-47 · Zbl 0343.41011
[2] de Boor, C., Odd-degree spline interpolation at a biinfinite knot sequence, (Schaback, R.; Scherer, K., Approximation Theory. Approximation Theory, Lecture Notes in Mathematics No. 556 (1976), Springer-Verlag: Springer-Verlag New York), 30-51 · Zbl 0337.41004
[3] de Boor, C., On local linear functionals which vanish at all \(B\)-splines but one, (Law, A. G.; Sahney, B. N., Theory of Aproximation with Applications (1976), Academic Press: Academic Press New York), 120-145 · Zbl 0346.41007
[4] de Boor, C.; Fix, G., Spline approximation by quasi-interpolants, J. Approximation Theory, 8, 19-45 (1973) · Zbl 0279.41008
[5] Demko, S., Local approximation properties of spline projections, J. Approximation Theory, 19, 176-185 (1977) · Zbl 0361.41019
[6] Demko, S., Inverses of band matrices and local convergence of spline projections, SIAM J. Numer. Anal., 14, 616-619 (1977) · Zbl 0367.65024
[7] De Vore, R., Degree of approximation, (Lorentz, G. G.; Chui, C. K.; Schumaker, L. L., Approximation Theory II (1976), Academic Press: Academic Press New York), 117-161
[8] Jerome, J. W., On uniform approximation by certain generalized spline functions, J. Approximation Theory, 7, 143-154 (1973) · Zbl 0252.41010
[9] Jerome, J. W.; Schumaker, L. L., On Lg-splines, J. Approximation Theory, 2, 29-49 (1969) · Zbl 0172.34501
[10] Jerome, J. W.; Schumaker, L. L., Local support basis for a class of spline functions, J. Approximation Theory, 16, 16-27 (1976) · Zbl 0342.41008
[11] Jerome, J. W.; Varga, R. S., Generalizations of spline functions and applications to nonlinear boundary value and eigenvalue problems, (Greville, T. N.E, Theory and Applications of Spline Functions (1969), Academic Press: Academic Press New York), 103-155 · Zbl 0188.13004
[12] Johnen, H.; Scherer, K., Direct and inverse theorems for best approximation by Λ-splines, (Böhmer, K.; Meinardus, G.; Schempp, W., Spline Functions. Spline Functions, Lecture Notes in Mathematics No. 501 (1975), Springer-Verlag: Springer-Verlag New York), 116-131 · Zbl 0318.41005
[13] Karlin, S., (Total Positivity, Vol. 1 (1968), Stanford Univ. Press: Stanford Univ. Press Stanford, Calif) · Zbl 0219.47030
[14] Lyche, T.; Schumaker, L. L., Local spline approximation methods, J. Approximation Theory, 15, 294-325 (1975) · Zbl 0315.41011
[15] Marsden, M., An identity for spline functions with applications to variation diminishing spline approximation, J. Approximation Theory, 3, 7-49 (1970) · Zbl 0192.42103
[16] Schumaker, L. L., Toward a constructive theory of generalized spline functions, (Böhmer, K.; Meinardus, G.; Schempp, W., Spline Functions. Spline Functions, Lecture Notes in Mathematics No. 501 (1975), Springer-Verlag: Springer-Verlag New York), 265-331
[17] Schumaker, L. L., On Tchebycheffian spline functions, J. Approximation Theory, 18, 278-303 (1976) · Zbl 0339.41004
[18] Swartz, B. K.; Varga, R. S., Error bounds for spline and L-spline interpolation, J. Approximation Theory, 6, 6-49 (1972) · Zbl 0242.41008
[19] Varga, R. S., Error bounds for spline approximation, (Schoenberg, I. J., Approximation Theory with Special Emphasis on Spline Functions (1969), Academic Press: Academic Press New York), 367-388
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