Propagation of errors for matrix inversion

Abstract

A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 × 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.

Measurement of the branching fractions and mass spectra for τ lepton decays including KS0 at Belle

“…These uncertainties are integrated into the efficiency migration matrix [5]. The uncertainties from the decay model implemented into the τ MC sample are estimated by using weighting sets of MC samples generated with different hadron decay models.…”

A Simultaneous Measurement of the Branching Fractions of Ten B to Double Charm Decays

“…With all the ingredients C, P and D in place, we can now use Equation To propagate the errors of the cross feed matrix, we use the formula [29]:…”

Tau decays with neutral kaons

“…In addition, there are straightforward contributions from the limited statistics of the Monte Carlo samples used to estimate the selection efficiencies and from the uncertainties on the bias factors. The systematic error on the branching ratios due to the Monte Carlo statistics is calculated directly from the statistical uncertainties on the elements of the inverse efficiency matrix [12]. The systematic error on each branching ratio due to the bias factor is calculated directly from the bias factor error.…”