## RSICC CODE PACKAGE CCC-787

### 1. NAME AND TITLE

EXPALS: Least Square Fit of
Linear Combination of Exponential Decay Function

### 2. CONTRIBUTORS

Lawrence Livermore Laboratory Livermore, California, USA through
the NEADB.

### 3. CODING LANGUAGE AND COMPUTER

Fortran 4 CDC7600 (C00787C760000).

### 4. NATURE OF PROBLEM SOLVED

This program fits by least squares a function which is a
linear combination of real exponential decay functions. The function is y(k) =
summation over j of a(j) * exp(-lambda(j) * k). Values of the independent
variable (k) and the dependent variable y(k) are specified as input data.
Weights may be specified as input information or set by the program (w(k) =
1/y(k)).

### 5. METHOD OF SOLUTION

The Prony-Householder iteration method is used. For
unequally-spaced data, a number of interpolation options are provided. This
revision includes an option to call a differential correction subroutine REFINE
to improve the approximation to unequally-spaced data when equal-interval
interpolation is faulty. If convergence is achieved, the probable errors in the
computed parameters are calculated also.

### 6. RESTRICTIONS OR LIMITATIONS

Generally, it is desirable to have at least 10n observations
where n equals the number of terms and to input k+n significant figures if k
significant figures are expected.

### 7. TYPICAL RUNNING TIME

Run times vary based on system, on the order of a few
seconds.

### 8. COMPUTER HARDWARE REQUIREMENTS

CDC 7600.

### 9. COMPUTER SOFTWARE REQUIREMENTS

A legacy Fortran 4 compiler, however, with editing, a
Fortran77 compiler should also work.

### 10. REFERENCES

C. Douglas Gardner, *EXPALS-FORTRAN Code for Exponential
Approximation by Least Squares*, Lawrence Livermore Laboratory report UCRL-14541,
Rev. 2 (August 1, 1978) Livermore, California.

R. E. von Holdt, “Minimize Linear Residuals,” LLL Computer
Information Center Report F3-001 (March 1969).

J. D. Lawrence, “Polynomial Root Finder,” LLL Computer Information
Center Report C2.2-001 (December 16, 1966).

A. S. Householder, *On Prony's Method of Fitting Exponential
Decay Curves and Multiple-Hit Survival Curves*, Oak Ridge National
Laboratory report ORNL-455 (February 3, 1950).

### 11. CONTENTS OF CODE PACKAGE

Included are the referenced documents, source, data, and sample
input and output files in a self-extracting executable on CD.

### 12. DATE OF ABSTRACT

November 2011.

**KEYWORDS**: RADIOACTIVITY