Sample matrix inversion (or direct matrix inversion) is an algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

 that estimates weights of an array (adaptive filter

Adaptive filter

An adaptive filter is a filter that self-adjusts its transfer function according to an optimization algorithm driven by an error signal. Because of the complexity of the optimization algorithms, most adaptive filters are digital filters. By way of contrast, a non-adaptive filter has a static...

) by replacing the correlation matrix R_u with its estimate. Using K samples , an unbiased estimate of R_u, the correlation matrix of the array signals, may be obtained by means of a simple averaging scheme:
The expression of the theoretically optimal weights requires the inverse

Inverse

Inverse may refer to:* Inverse , a type of immediate inference from a conditional sentence* Inverse , a program for solving inverse and optimization problems...

of R_u, and the inverse of the estimates matrix is then used for finding estimated optimal weights.