Numerische Mathematik

, Volume 15, Issue 5, pp 359–370 | Cite as

A generalization ofL-splines

  • Thomas R. Lucas
Article

Abstract

A theory of generalized splines is developed for all regular formally self adjoint differential operatorsL with real coefficients. A special case of such operators are those which may be factored in the formL =L 1 * L1, such as those related to the generalized splines of Ahlberg, Nilson, and Walsh [1, 2], and theL-splines of Schultz and Varga [6]. Theorems giving unique interpolation, integral relations, and convergence rates are established. IfL has a certain positivity property, a useful extremal result is proven.

Keywords

Convergence Rate Mathematical Method Positivity Property Integral Relation Real Coefficient 

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References

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    Ahlberg, J. H., Nilson, E. N., Walsh, J. L.: Fundamental properties of generalized splines. Proc. Nat. Acad. Sci. U.S.A.52, 1412–1419 (1964).Google Scholar
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    Ciarlet, P. G., Schultz, M. H., Varga, R. S.: Numerical methods of high-order accuracy for nonlinear boundary value problems. I. One dimensional problem. Numer. Math.9, 394–430 (1967).Google Scholar
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    Coddington, E. A., Levinson, N.: Theory of ordinary differential equations. New York: McGraw-Hill Book Co. 1955.Google Scholar
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    Schultz, M. H., Varga, R. S.:L-splines. Numer. Math.10, 345–369 (1967).Google Scholar

Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Thomas R. Lucas
    • 1
  1. 1.Department of MathematicsThe University of North Carolina at CharlotteCharlotte

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