FORTRAN Subroutines for Bicubic Spline Interpolation

Abstract

Two CDC 3800 FORTRAN subroutines (BICUB1 and BICUB2) which perform bicubic spline interpolation of a tabulated function of two variables are described. Given the values X(1),...,X(N) and Y(1),...,Y(M) of two independent variables and the corresponding function values U(I,J)=f(X(I), Y(J)), I=1,...,N and J=1,...,M and certain normal derivatives (optional) along the boundaries of the x-y mesh, BICUB1 estimates the derivatives f(x), f(y), and f(xy) at each (I, J) mesh point. If the normal derivatives along the mesh boundaries are unknown, BICUB1 estimates them using a moving third order two dimensional Lagrange interpolating polynomial. Given the coordinates (XPT, YPT) and the derivatives calculated by BICUB1, BICUB2 obtains the coefficients of the bicubic polynomial for the rectangular region of the mesh containing (XPT, YPT) and estimates the functional value UPT=f(XPT,YPT). In effect, the routines pass a twice continuously differentiable piecewise bicubic polynomial, u(x,y) belongs to (C sup 2), through the given functional values.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1973
Accession Number
AD0762419

Entities

People

  • John J. Cornyn

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Advanced Electronics
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Coefficients
  • Computer Programming
  • Computer Programs
  • Computers
  • Information Processing
  • Interpolation
  • Language
  • Linear Systems
  • Mathematics
  • Military Research
  • Numerical Analysis
  • Operating Systems
  • Polynomials
  • Procedures (Computers)
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Approximation Theory.