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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

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
Creator
Contributor
Author
Publisher
Subject
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 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
Member of
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
1917-2010
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
Instantiates
Publication
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 177-ERL 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
Publication
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 177-ERL 186.
Other physical details
illustrations
System control number
(OCoLC)4521442

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