In Equation 19, D (= [d.sub.cal]), \ is the

matrix inversion operator and r' is the transpose of the vector consisting receivers at spatial positions and Q is the source vector.

It requires [U.sup.2] multiplications and O([U.sup.3])

matrix inversion.

It covers approximations and errors in computation, the solution of algebraic and transcendental equations, the solution of simultaneous algebraic equations, the

matrix inversion and eigenvalue problem, empirical laws and curve-fitting, finite differences, interpolations, numerical differentiation and integration, difference equations, the numerical solution of ordinary differential equations, the numerical solution of partial differential equations, linear programming, and a brief review of computers.

However, these methods inevitably involve complicated

matrix inversion due to the large dimensions of massive MIMO systems, resulting in highly burdensome complexity in practice.

Indeed, a problem of the

matrix inversion is encountered.

Though ZF algorithm is simple, the

matrix inversion associated with this algorithm is highly expensive as the number of user antennas increases.

Direct material decomposition via

matrix inversion is a way of calculating the points *1 and *2 in the decomposed image, which is written as follows:

The main advantage of algebraic methods is that they can provide a simple algebraic solution without the computation of

matrix inversion which makes those methods can be applied in a low-cost location system especially for wireless sensor networks (WSNs) [5, 20].

The notion of the need for efficient schemes is the fact that (5) is slow at its initial stage of iterates, and this would increase the computational burdensome of the scheme applied for

matrix inversion.

It should be noted that (17) does not require any

matrix inversion under the assumption that all users' data is independent from each other and they have a common covariance matrix.

It requires simultaneous equations, a coefficient matrix,

matrix inversion, and matrix multiplication to get the cost allocations.

Other proposed approaches use different strategies to decrease the cost of

matrix inversion. In [15], a scheme based on the Gauss-Seidel method is used; nevertheless, it remains necessary to compute at least one

matrix inversion, which may result in instability for large matrices.