Propagation of Errors for Matrix Inversion
M. Lefebvre, R.K. Keeler, R. Sobie, J. White
TL;DR
This paper presents a formula for error propagation in matrix inversion, compares it with Monte Carlo methods, and provides criteria for assessing the reliability of covariance calculations for uncertain matrices.
Contribution
It introduces an explicit error propagation formula for matrix inversion and offers a practical prescription to evaluate the reliability of covariance estimates.
Findings
The error propagation formula matches Monte Carlo results for 2x2 matrices.
A criterion is provided to determine when covariance calculations are reliable.
The method helps assess the impact of element uncertainties on inverted matrices.
Abstract
A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with uncertain elements is sufficiently nonsingular for the calculation of the covariances of the inverted matrix elements to be reliable.
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