Cholesky Factorization and Matrix Inversion

Cholesky Factorization and Matrix Inversion PDF

Author: Erwin Schmid

Publisher:

Published: 1973

Total Pages: 24

ISBN-13:

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The Cholesky square root algorithm used in the solution of linear equations with a positive definite matrix of coefficients is developed by elementary matrix algebra, independent of the Gaussian elimination from which it was originally derived. The Cholesky factorization leads to a simple inversion procedure for the given matrix. A simple transformation makes the inversion applicable to nonsymmetric matrices. The least squares hypothesis is shown to be the simplest and most general unique solution of a system of linear equations with a nonsquare matrix of coefficients. The method of proof is extended to develop the Gaussian elimination algorithm in a readily comprehensible procedure.

A Cross-coupling Computer for the Oceanographer's Askania Gravity Meter

A Cross-coupling Computer for the Oceanographer's Askania Gravity Meter PDF

Author: Carl A. Pearson

Publisher:

Published: 1974

Total Pages: 28

ISBN-13:

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A cross-coupling computer has been built for the NOAA ship Oceanographer's Askania GSS 2 gravity meter. Beam deflection and surge acceleration signals are obtained, respectively, from the gravity meter and its associated Anshutz gyro table. These are multiplied electronically and filtered to give computed cross-coupling error. Cross-coupling error is recorded on an analog recorder, and encoded for processing by the shipboard computer. Comparison of trackline crossings where significant cross coupling was recorded showed that the average crossing discrepancy was reduced from 14.5 milligals (mgal) to 2.5 mgal when corrected. On a traverse of the Cape Flattery gravity range, gravity error was reduced from an average of about 12 mgal to about 1 mgal by correcting for cross coupling.

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