Convergence Of Iterative Methods Applied To Large Overdetermined Linear And Nonlinear Systems Of Equations Using Least Squares

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Convergence Of Iterative Methods Applied To Large Overdetermined Linear And Nonlinear Systems Of Equations Using Least Squares

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Author : Charles O. Stearns
language : en
Publisher:
Release Date : 1970

Convergence Of Iterative Methods Applied To Large Overdetermined Linear And Nonlinear Systems Of Equations Using Least Squares written by Charles O. Stearns and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Chebyshev polynomials categories.

Solutions are obtained to large overdetermined systems of equations. Both nonlinear and linear systems are considered. The nonlinear system represents a dipole model of the earth's geomagnetic field, which is generated from spherical harmonic coefficients. This system of 64 unknowns and 1836 equations is solved by a maximum neighborhood method, which is an optimum interpolation between the well known Taylor's series and steepest descent methods. The original given values of the generated field are as large as 60,000 gamma, whereas a rms residual of 27.9 gamma is obtained with 173 iterations. The linear system of equations represents dipole changes required to account for the earth's secular change field which is generated from spherical harmonic coefficients. The dipole parameters computed from the nonlinear model are used as input parameters. The system contains 64 unknowns and 612 equations and is solved using a Chebyshev polynomial iterative method. These results are compared to results obtained by a direct solution of the normal equations of the system and results obtained by a pseudo-inverse method using a modified Gram-Schmidt factorization. Although the latter two methods give smaller rms values than the iterative method, the results of the iterative method are more reasonable in view of known properties of the results. The generated field has a rms value of 45 gamma per year. An rms residual of 2.5 gamma per year was obtained after 25,000 iterations.

Convergence Of Iterative Methods Applied To Large Overdetermined Linear And Nonlinear Systems Of Equations Using Least Squares

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Author : Charles O. Stearns
language : en
Publisher:
Release Date : 1970

Convergence Of Iterative Methods Applied To Large Overdetermined Linear And Nonlinear Systems Of Equations Using Least Squares written by Charles O. Stearns and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Equations categories.

Essa Technical Report Erl Esl

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Author :
language : en
Publisher:
Release Date : 1967

Essa Technical Report Erl Esl written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Earth sciences categories.

Essa Technical Report Erl

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Author : United States. Environmental Science Services Administration
language : en
Publisher:
Release Date : 1970

Essa Technical Report Erl written by United States. Environmental Science Services Administration and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.

Noaa Technical Report Erl

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Author : United States. National Oceanic and Atmospheric Administration
language : en
Publisher:
Release Date : 1972

Noaa Technical Report Erl written by United States. National Oceanic and Atmospheric Administration and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.

Monthly Catalogue United States Public Documents

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Author :
language : en
Publisher:
Release Date : 1970

Monthly Catalogue United States Public Documents written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Government publications categories.

Research In Progress

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Author :
language : en
Publisher:
Release Date : 1978

Research In Progress written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Military research categories.

Monthly Catalog Of United States Government Publications

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Author : United States. Superintendent of Documents
language : en
Publisher:
Release Date : 1966

Monthly Catalog Of United States Government Publications written by United States. Superintendent of Documents and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Government publications categories.

Monthly Catalog Of United States Government Publications Cumulative Index

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Author : United States. Superintendent of Documents
language : en
Publisher:
Release Date : 1970

Monthly Catalog Of United States Government Publications Cumulative Index written by United States. Superintendent of Documents and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with United States categories.

Scientific And Technical Aerospace Reports

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Author :
language : en
Publisher:
Release Date : 1981

Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Aeronautics categories.