Polynomial Splines

  • Richard E. Bellman
  • Robert S. Roth
Part of the Mathematics and Its Applications book series (MAIA, volume 26)


In the last chapter we considered two very simple polynomials as approximating functions, the segmented straight line over the closed interval (0,1), and the set of 27 orthogonal quadratic polynomials over the unit cube, −1 ≤ ξ,η,ζ ≤ 1.


Recursion Relation Mesh Point Segmented Straight Line Minimization Procedure Polynomial Spline 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography and Comments

  1. Alhberg, J.H.,E.N. Nilson and J.L. Walsh,:1967, The Theory of Splines and Their Applications, Academic Press, N.Y.zbMATHGoogle Scholar
  2. Gersgorin, S.:1941, “Uber die Abgrenzung die Eigenwerte einer Martix”, Izv. Akad.Nauk SSSR. ser.Mat., 7, 749–753Google Scholar
  3. Todd, J.:1962, A Survey of Numerical Analysis McGraw-Hill Book Co, N.Y.Google Scholar
  4. Potter, M.L.:1955, “ A Matrix Method for the Solution of a Second Order Difference Equation in two Variables”’ Math Centrum Report, MR19Google Scholar
  5. Bellman, R., B.G. Kashef and R. Vasdevan,:1973, “Splines via Dynamic Programming”, JMAA, 38,2, 427–430Google Scholar
  6. Bellman, R., B.G. Kashef and R. Vasudevan,:1973, “A Note on Mean Square Spline Approximation”, JMAA 42,2 47–53MathSciNetGoogle Scholar
  7. Bellman, R., B.G. Kashef, R. Vasudevan, and E.S. Lee,:1975, “Differential Quadrature and Splines”, Computers and Mathematics with Applications, vol 1,3/4, 372–376MathSciNetGoogle Scholar
  8. Bellman, R. and R.S. Roth,:1971, “The Use of Splines with Unknown End Points in the Identification of Systems”, JMAA, 34,1, 26–33MathSciNetzbMATHGoogle Scholar
  9. Holladay, J.C.:1957, “Smoothest Curve Approximation”, Math Tables Aids to Computation,11, 233–267Google Scholar

Copyright information

© D Reidel Publishing Company 1986

Authors and Affiliations

  • Richard E. Bellman
    • 1
    • 2
  • Robert S. Roth
    • 3
  1. 1.Department of Electrical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Center for Applied MathematicsThe University of GeorgiaAthensUSA
  3. 3.BostonUSA

Personalised recommendations