Computer Programs
NEA-0367 APPROX.
last modified: 01-AUG-1975 | catalog | categories | new | search |

NEA-0367 APPROX.

APPROX, 1-D and 2-D Function Approximation by Polynomials, Splines, Finite Elements Method

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1. NAME OR DESIGNATION OF PROGRAM:  APPROX.
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2. COMPUTERS
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Program name Package id Status Status date
APPROX NEA-0367/01 Tested 01-AUG-1975

Machines used:

Package ID Orig. computer Test computer
NEA-0367/01 IBM 370 series IBM 370 series
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3. NATURE OF PHYSICAL PROBLEM SOLVED

Approximates one- and two- dimensional functions using different forms of the approximating function, as polynomials, rational functions, splines and (or) the finite element method. Different kinds of transformations of the dependent and (or) the independent variables can easily be made by data cards using a FORTRAN-like language.
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4. METHODS

METHOD OF SOLUTION.
Approximations by polynomials, splines and (or) the finite element method are made in L2 norm using the least square method by  which the answer is directly given. For rational functions in one dimension the result given in L(infinite) norm is achieved by iterations moving the zero points of the error curve. For rational functions in two dimensions, the norm is L2 and the result is achieved by iteratively changing the coefficients of the denominator and then solving the coefficients of the numerator by the least square method.
The transformation of the dependent and (or) independent variables is made by compiling the given transform data card(s) to an array of integers from which the transformation can be made.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
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6. TYPICAL RUNNING TIME

TYPICAL RUNNING TIME. Proportional to the complexity of the approximation expression and the number of given points.
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7. UNUSUAL FEATURES: UNUSUAL FEATURES OF THE PROGRAM
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8. RELATED OR AUXILIARY PROGRAMS: RELATED AND AUXILIARY PROGRAMS
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9. STATUS
Package ID Status date Status
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10. REFERENCES
NEA-0367/01, included references:
- B. Tollander:
APPROX, A Programme for Getting Polynomial and Rational
Approximations of Functions
AB Atomenergi AE-RD-28 (17.3.71).
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11. HARDWARE REQUIREMENTS: MACHINE REQUIREMENTS
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NEA-0367/01 FORTRAN-IV
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13. OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED:  DOS, release 25, and O.S.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

ANY OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS
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15. NAME AND ESTABLISHMENT OF AUTHOR

Bengt Tollander
AB Atomenergi
Fack
S-611 01 Nykoeping
Sweden.
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16. MATERIAL AVAILABLE
NEA-0367/01
File name File description Records
NEA0367_01.001 SOURCE PROGRAM (F4) EBCDIC 2773
NEA0367_01.002 SAMPLE PROBLEM DATA 223
NEA0367_01.003 JCL 7
NEA0367_01.004 SAMPLE PROBLEM PRINTED OUTPUT 1037
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17. CATEGORIES
• P. General Mathematical and Computing System Routines

Keywords: finite element method, iterative methods, least square fit, one-dimensional, polynomials, spline functions, two-dimensional.