Maximum Likelihood Nonlinear Correlated Fields (Battelle-Northwest Program Likely).

Duane, B.H.

doi:10.2172/4496648

Cited by 11 publications

(17 citation statements)

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“…The parameters ~ are computed at each successive iteration using the basic iterative algOrithm (2) (1)…”

Section: Methods Of Fittingmentioning

confidence: 99%

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GSSLRN-Ii: A Least-Squares Computer Code for the Analysis of Peak Shapes Which Can Be Defined Analytically.

Seybold¹

1971

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A computer code, GSSLRN-II, is presented which is written in generalized form so as to allow analysis of any data containing peak shapes which can be adequately represented by an analytical function form. GSSLRN-II utilizes a second order Newton-Raphson least-squaresiterative scheme in its analysis of peak shapes. Effect~ve use has been made of the measurement variance and the least-squares deviations to justify automatic recycling attempts of least-squares fits on groups of peaks.The code will locate peaks, group them in appropriate sets, optimize the interval-of-fit, least-squares fit the set of peaks, recycle for another fit if necessary, and upon ootion will generate plots of thp fitted results. ~1any other options are available which allm'l the user a high degree of versatility \'lith respect to input and/or output options.• . -• ".'• . . I. I ntrodu cti on BNWL-1579 GSSLRN-I I A LEAST-SQUARES COMPUTER CODE FOR THE ANALYSIS OF PEAK SHAPES WHICH CAN BE DEFINED ANALYTICALLYA computer code, GSSLRN-II, is presented which is written in generalized form so as to allow analysis of any data containing peak shapes which can be adequately represented by an analytical function form.GSSLRN-II is a much more versatile code than GSSLRN-I (1) because it is not limited to the analyses of fission-product data using a fixed analytical function. In addition, GSSLRN-II contains a major improvement with respect to the use of measurement variance obtained from the least-squares fits for the purpose of justifying recycle (multiple fitting) attempts.The code makes use of the least-squares package, LEARN,(2,3) which utilizes a second order Taylors' expansion in its least-squares iterative scheme.The code contains a wide variety of options which are designed to allow the analyst many override features with respect to the input and/or output options.The net result is a code which is adaptable to many types of data with a minimal amount of necessary modification. [. Highlights of the Code Some of the features of GSSLRN-II which allow a wide variety of application are:• Ability to rewrite the analytical function which describes a continuum under the peak shapes without destroying the integrity of the code• Use of nonlinear least-squares techniques accompanied by a substantial regression analysis• Judicious use of the measurement variance in order to quantify the performance of a fit• An. automatic recycling logic which enables the code to build in hidden or unaccounted for peaks• Optional use of a peak searching routine(4) to locate peaks from data spectra collected on large multichannel analyzers• Optional input and/or output specifications including automatic on-line or off-line plotting features• CALCOMP plotting-options which display the measured s~ectr~m, fitted curves and their root-mean-square deviation envelope, fitted parameters, curves of each peak as they are resolved from a multf~let, or a three-dimensional plot of multiple spectra• No prior knowledge required to locate and successfully fit hidden or overlapping spectral c...

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“…The parameters ~ are computed at each successive iteration using the basic iterative algOrithm (2) (1)…”

Section: Methods Of Fittingmentioning

confidence: 99%

“…The code makes use of the least-squares package, LEARN, (2,3) which utilizes a second order Taylors' expansion in its least-squares iterative scheme.…”

Section: Introduction Bnwl-1579 Gsslrn-i I a Least-squares Compmentioning

confidence: 99%

GSSLRN-Ii: A Least-Squares Computer Code for the Analysis of Peak Shapes Which Can Be Defined Analytically.

Seybold¹

1971

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show abstract

“…Equation (1) shows that Q is then a quadratic function of ~ and that the contours of constant Q are ellipses. * The set of Equations (2) becomes linear and has a unique solution, which corresponds to the true minimum (barring singular cases).…”

Section: Linear Casementioning

confidence: 99%

“…Note that this is the equation of a paraboloid that is a local approximation of the true Q-surface defined by Equation (1). The iterative stepping logic uses the fact that the accuracy improves as da decreases.…”

Section: Anal Ys Is and Algebra Of The Nonl Inear Casementioning

confidence: 99%

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A Tandem Method for Finding Unconstrained Minima in Nonlinear Least-Squares Problems: Program Learn-I-C.

Kottwitz¹

1971

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Unfolding Particle Size Distributions

Nicholson

Merckx

1969

Technometrics

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Maximum Likelihood Nonlinear Correlated Fields (Battelle-Northwest Program Likely).

Cited by 11 publications

References 0 publications

GSSLRN-Ii: A Least-Squares Computer Code for the Analysis of Peak Shapes Which Can Be Defined Analytically.

GSSLRN-Ii: A Least-Squares Computer Code for the Analysis of Peak Shapes Which Can Be Defined Analytically.

A Tandem Method for Finding Unconstrained Minima in Nonlinear Least-Squares Problems: Program Learn-I-C.

Unfolding Particle Size Distributions

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