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Solution of Large Systems of Linear Equations with Quadratic or Non-Quadratic Matrices and Deconvoiution of Spectra

Abstract

The numerical deconvolution of spectra is equivalent to the solution of a (large) system of linear equations with a matrix which is not necessarily a square matrix. The demand that the square sum of the residual errors shall be minimum is not in general sufficient to ensure a unique or 'sound' solution. Therefore other demands which may include the demand for minimum square errors are introduced which lead to 'sound' and 'non-oscillatory' solutions irrespective of the shape of the original matrix and of the determinant of the matrix of the normal equations.
Authors:
Publication Date:
Dec 15, 1967
Product Type:
Technical Report
Report Number:
AE-307
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; SPECTRA UNFOLDING; MATHEMATICAL MODELS; MATRICES; LEAST SQUARE FIT; DATA COVARIANCES
OSTI ID:
20956289
Research Organizations:
AB Atomenergi, Nykoeping (Sweden)
Country of Origin:
Sweden
Language:
English
Other Identifying Numbers:
TRN: SE0708723
Availability:
Commercial reproduction prohibited; OSTI as DE20956289
Submitting Site:
SWDN
Size:
20 pages
Announcement Date:
Dec 29, 2007

Citation Formats

Nygaard, K. Solution of Large Systems of Linear Equations with Quadratic or Non-Quadratic Matrices and Deconvoiution of Spectra. Sweden: N. p., 1967. Web.
Nygaard, K. Solution of Large Systems of Linear Equations with Quadratic or Non-Quadratic Matrices and Deconvoiution of Spectra. Sweden.
Nygaard, K. 1967. "Solution of Large Systems of Linear Equations with Quadratic or Non-Quadratic Matrices and Deconvoiution of Spectra." Sweden.
@misc{etde_20956289,
title = {Solution of Large Systems of Linear Equations with Quadratic or Non-Quadratic Matrices and Deconvoiution of Spectra}
author = {Nygaard, K}
abstractNote = {The numerical deconvolution of spectra is equivalent to the solution of a (large) system of linear equations with a matrix which is not necessarily a square matrix. The demand that the square sum of the residual errors shall be minimum is not in general sufficient to ensure a unique or 'sound' solution. Therefore other demands which may include the demand for minimum square errors are introduced which lead to 'sound' and 'non-oscillatory' solutions irrespective of the shape of the original matrix and of the determinant of the matrix of the normal equations.}
place = {Sweden}
year = {1967}
month = {Dec}
}