Abstract
A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper.
Highlights
Computing the matrix inverse of nonsingular matrices of higher sizes is difficult and is a time consuming task
Target equations are modeled explicitly such that the position and velocity and potentially higher derivatives of each measurement are approximated by the track filter as a state vector
The approximated error with the state vector is modeled by taking into account a covariance matrix, which is used in subsequent computations
Summary
Computing the matrix inverse of nonsingular matrices of higher sizes is difficult and is a time consuming task. An example could be in phased-array radar whereas the target tracking is a recursive prediction correction process, when Kalman filtering is extensively consumed; see [2, 3]. Target equations are modeled explicitly such that the position and velocity and potentially higher derivatives of each measurement are approximated by the track filter as a state vector. The approximated error with the state vector is modeled by taking into account a covariance matrix, which is used in subsequent computations. Finding the inverse in the iteration could make use of the inverse in the present iteration. In this circumstance, fast and efficient iterative algorithms are required
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