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References
G. Birkhoff ɛ D. de Boor, Error bounds for spline interpolation, J.Math.Mech. 13 (1964) 827–836
C. de Boor, On uniform approximation by splines, J.Approximation Theory 1 (1968) 219–235
", The quasi-interpolant as a tool in elementary polynomial spline theory, in "Approximation Theory", G.G. Lorentz ed., Academic Press, New York, 1973, 269–276
", On bounding spline interpolation, J.Approximation Theory 14 (1975) 191–203
", How small can one make the derivatives of an interpolating function?, J.Approximation Theory 13 (1975) 105–116
", On cubic spline functions that vanish at all knots, MRC TSR 1424, May 1974; Adv.Math. 20 (1976) 1–17
", A bound on the
-norm of
-approximation by splines in terms of a global mesh ratio, MRC TSR 1597, Aug. 1975; Math. Comp. 30 (1976)", ɛ I.J. Schoenberg, Cardinal interpolation and spline functions VIII. The Budan-Fourier theorem for splines and applications, in "Spline functions, Karlsruhe 1975", Springer Lecture Notes in Mathematics 501, Springer, Berlin, 1976, 1–79
H.B. Curry ɛ I.J. Schoenberg, On Pólya frequency functions IV. The fundamental spline functions and their limits, J.d'Analyse Math. 17 (1966) 71–107
S. Demko, Inverses of band matrices and local convergence of spline projections, Feb. 1976; to appear in SIAM J.Numer.Anal.
J. Descloux, On finite element matrices, SIAM J.Numer.Anal. 9 (1972) 260–265
J. Douglas, Jr., T. Dupont ɛ L. Wahlbin, Optimal
-error estimates for Galerkin approximations to solutions of two point boundary value problems, Math.Comp. 29 (1975) 475–483S. Friedland ɛ C. A. Micchelli, Bounds on the solution of difference equations and spline interpolation at knots, to appear
C. A. Micchelli, Oscillation matrices and cardinal spline inter-polation, in "Studies in spline functions and approximation theory" by S. Karlin, C. Micchelli, A. Pinkus and I.J. Schoenberg, Academic Press, New York, 1976, 163–201
I.J. Schoenberg, Cardinal interpolation and spline functions, J. Approximation Theory 2 (1969) 167–206
", Cardinal interpolation and spline functions II., J.Approximation Theory 6 (1972) 404–420
Ju. N. Subbotin, On the relations between finite differences and the corresponding derivatives, Proc.Steklov Inst.Mat. 78 (1965) 24–42; Engl.Transl. by Amer.Mathem.Soc. (1967) 23–42
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de Boor, C. (1976). Odd-degree spline interpolation at a biinfinite knot sequence. In: Schaback, R., Scherer, K. (eds) Approximation Theory. Lecture Notes in Mathematics, vol 556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087395
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DOI: https://doi.org/10.1007/BFb0087395
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-norm of
-approximation by splines in terms of a global mesh ratio, MRC TSR 1597, Aug. 1975; Math. Comp. 30 (1976)
-error estimates for Galerkin approximations to solutions of two point boundary value problems, Math.Comp. 29 (1975) 475–483