The Resource Convergence of iterative methods applied to large overdetermined linear and nonlinear systems of equations using least squares, Charles O. Stearns, Leroy R. Alldredge
Convergence of iterative methods applied to large overdetermined linear and nonlinear systems of equations using least squares, Charles O. Stearns, Leroy R. Alldredge
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The item Convergence of iterative methods applied to large overdetermined linear and nonlinear systems of equations using least squares, Charles O. Stearns, Leroy R. Alldredge represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Convergence of iterative methods applied to large overdetermined linear and nonlinear systems of equations using least squares, Charles O. Stearns, Leroy R. Alldredge represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 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 pseudoinverse method using a modified GramSchmidt 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
 Language
 eng
 Extent
 iii, 12 pages
 Note
 "August 1970."
 Label
 Convergence of iterative methods applied to large overdetermined linear and nonlinear systems of equations using least squares
 Title
 Convergence of iterative methods applied to large overdetermined linear and nonlinear systems of equations using least squares
 Statement of responsibility
 Charles O. Stearns, Leroy R. Alldredge
 Subject

 Equations  Numerical solutions
 Equations  Numerical solutions
 Equations  Numerical solutions
 Geomagnetism  Mathematical models
 Geomagnetism  Mathematical models
 Geomagnetism  Mathematical models
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 Least squares
 Least squares
 Least squares
 Magnetic anomalies
 Magnetic anomalies
 Magnetic anomalies
 Chebyshev polynomials
 Chebyshev polynomials
 Chebyshev polynomials
 Language
 eng
 Summary
 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 pseudoinverse method using a modified GramSchmidt 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
 Cataloging source
 RRR
 http://library.link/vocab/creatorName
 Stearns, Charles O
 Government publication
 federal national government publication
 Illustrations
 illustrations
 Index
 no index present
 LC call number
 QA218
 LC item number
 .S8
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 19172010
 http://library.link/vocab/relatedWorkOrContributorName

 Alldredge, L. R.
 Earth Sciences Laboratories (U.S.)
 United States
 Series statement

 ESSA technical report ERL
 ESL
 Series volume

 181.
 10
 http://library.link/vocab/subjectName

 Geomagnetism
 Least squares
 Magnetic anomalies
 Chebyshev polynomials
 Equations
 Iterative methods (Mathematics)
 Magnetic anomalies
 Chebyshev polynomials
 Least squares
 Geomagnetism
 Equations
 Iterative methods (Mathematics)
 Label
 Convergence of iterative methods applied to large overdetermined linear and nonlinear systems of equations using least squares, Charles O. Stearns, Leroy R. Alldredge
 Note
 "August 1970."
 Bibliography note
 Includes bibliographical references (page 12)
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 4521442
 Dimensions
 28 cm.
 Extent
 iii, 12 pages
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Note
 MU: Bound with numbers in series: ESSA technical report, ERL 177ERL 186.
 Other physical details
 illustrations
 System control number
 (OCoLC)4521442
 Label
 Convergence of iterative methods applied to large overdetermined linear and nonlinear systems of equations using least squares, Charles O. Stearns, Leroy R. Alldredge
 Note
 "August 1970."
 Bibliography note
 Includes bibliographical references (page 12)
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 4521442
 Dimensions
 28 cm.
 Extent
 iii, 12 pages
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Note
 MU: Bound with numbers in series: ESSA technical report, ERL 177ERL 186.
 Other physical details
 illustrations
 System control number
 (OCoLC)4521442
Subject
 Equations  Numerical solutions
 Equations  Numerical solutions
 Equations  Numerical solutions
 Geomagnetism  Mathematical models
 Geomagnetism  Mathematical models
 Geomagnetism  Mathematical models
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 Least squares
 Least squares
 Least squares
 Magnetic anomalies
 Magnetic anomalies
 Magnetic anomalies
 Chebyshev polynomials
 Chebyshev polynomials
 Chebyshev polynomials
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Convergenceofiterativemethodsappliedtolarge/GvjZKLEJcyw/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Convergenceofiterativemethodsappliedtolarge/GvjZKLEJcyw/">Convergence of iterative methods applied to large overdetermined linear and nonlinear systems of equations using least squares, Charles O. Stearns, Leroy R. Alldredge</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>