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Conjugate gradient analysis: A new tool for studying satellite magnetic data sets
Author(s) -
Purucker Michael E.,
Sabaka Terence J.,
Langel Robert A.
Publication year - 1996
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/96gl00388
Subject(s) - conjugate gradient method , computer science , nonlinear conjugate gradient method , satellite , algorithm , conjugate residual method , matrix (chemical analysis) , gradient method , earth's magnetic field , transformation (genetics) , iterative method , derivation of the conjugate gradient method , sparse matrix , magnetic dipole , inverse problem , mathematics , dipole , magnetic field , physics , mathematical analysis , gradient descent , materials science , chemistry , composite material , biochemistry , quantum mechanics , machine learning , artificial neural network , gaussian , astronomy , gene
Conjugate gradient and sparse matrix techniques are utilized in the solution of a geomagnetic inverse problem. Global crustal data sets collected from low‐earth orbit are quickly inverted (using a design matrix approach) or continued to a common altitude (using a normal matrix approach) even when using parameterizations of 10,000 or more dipoles. The sparsity results from the rapid decay of the magnetic field with distance from the dipole. Iterative techniques such as the conjugate gradient save computer time and space when compared to more direct approaches using the Householder transformation, thus allowing problems that were intractable to all but the largest supercomputers to be performed on workstations of only moderate power.