NEA-0367 APPROX.

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

NAME OR DESIGNATION OF PROGRAM, COMPUTER, NATURE OF PHYSICAL PROBLEM SOLVED, SOLUTION, RESTRICTIONS, CPU, FEATURES, AUXILIARIES, STATUS, REFERENCES, REQUIREMENTS, LANGUAGE, OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED, OTHER RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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1. NAME OR DESIGNATION OF PROGRAM: APPROX.

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2. COMPUTERS

To submit a request, click below on the link of the version you wish to order. Only liaison officers are authorised to submit online requests. Rules for requesters are available here.

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
NEA-0367/01	01-AUG-1975	Tested at NEADB

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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.