Abstract
From the point of view that no mathematical method can ever minimise or alter errors already made in a physical measurement, the classical least squares method has severe limitations which makes it unsuitable for the statistical analysis of many physical measurements. Based on the assumptions that the experimental errors are characteristic for each single experiment and that the errors must be properly estimated rather than minimised, a new method for solving large systems of linear equations is developed. The new method exposes the entire range of possible solutions before the decision is taken which of the possible solutions should be chosen as a representative one. The choice is based on physical considerations which (in two examples, curve fitting and unfolding of a spectrum) are presented in such a form that a computer is able to make the decision, A description of the computation is given. The method described is a tool for removing uncertainties due to conventional mathematical formulations (zero determinant, linear dependence) and which are not inherent in the physical problem as such. The method is therefore especially well fitted for unfolding of spectra.
Citation Formats
Nygaard, K.
Solution of Large Systems of Linear Equations in the Presence of Errors. A Constructive Criticism of the Least Squares Method.
Sweden: N. p.,
1968.
Web.
Nygaard, K.
Solution of Large Systems of Linear Equations in the Presence of Errors. A Constructive Criticism of the Least Squares Method.
Sweden.
Nygaard, K.
1968.
"Solution of Large Systems of Linear Equations in the Presence of Errors. A Constructive Criticism of the Least Squares Method."
Sweden.
@misc{etde_20956261,
title = {Solution of Large Systems of Linear Equations in the Presence of Errors. A Constructive Criticism of the Least Squares Method}
author = {Nygaard, K}
abstractNote = {From the point of view that no mathematical method can ever minimise or alter errors already made in a physical measurement, the classical least squares method has severe limitations which makes it unsuitable for the statistical analysis of many physical measurements. Based on the assumptions that the experimental errors are characteristic for each single experiment and that the errors must be properly estimated rather than minimised, a new method for solving large systems of linear equations is developed. The new method exposes the entire range of possible solutions before the decision is taken which of the possible solutions should be chosen as a representative one. The choice is based on physical considerations which (in two examples, curve fitting and unfolding of a spectrum) are presented in such a form that a computer is able to make the decision, A description of the computation is given. The method described is a tool for removing uncertainties due to conventional mathematical formulations (zero determinant, linear dependence) and which are not inherent in the physical problem as such. The method is therefore especially well fitted for unfolding of spectra.}
place = {Sweden}
year = {1968}
month = {Sep}
}
title = {Solution of Large Systems of Linear Equations in the Presence of Errors. A Constructive Criticism of the Least Squares Method}
author = {Nygaard, K}
abstractNote = {From the point of view that no mathematical method can ever minimise or alter errors already made in a physical measurement, the classical least squares method has severe limitations which makes it unsuitable for the statistical analysis of many physical measurements. Based on the assumptions that the experimental errors are characteristic for each single experiment and that the errors must be properly estimated rather than minimised, a new method for solving large systems of linear equations is developed. The new method exposes the entire range of possible solutions before the decision is taken which of the possible solutions should be chosen as a representative one. The choice is based on physical considerations which (in two examples, curve fitting and unfolding of a spectrum) are presented in such a form that a computer is able to make the decision, A description of the computation is given. The method described is a tool for removing uncertainties due to conventional mathematical formulations (zero determinant, linear dependence) and which are not inherent in the physical problem as such. The method is therefore especially well fitted for unfolding of spectra.}
place = {Sweden}
year = {1968}
month = {Sep}
}