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The ginv function calculates a pseudoinverse using the singular value decomposition provided by the svd function in the base R package. An alternative is to employ the pinv function available in the pracma package. The Octave programming language provides a pseudoinverse through the standard package function pinv and the pseudo_inverse() method.
In mathematics, a block matrix pseudoinverse is a formula for the pseudoinverse of a partitioned matrix. This is useful for decomposing or approximating many algorithms updating parameters in signal processing , which are based on the least squares method.
Note that differently from the feedback bits case, the required feedback resource is a function of both downlink and uplink channel conditions. It is reasonable to include the uplink channel status in the calculation of the feedback resource since the uplink channel status determines the capacity, i.e., bits/second per unit frequency band (Hz ...
Inverse transformation of Vaníček's LSSA is possible, as is most easily seen by writing the forward transform as a matrix; the matrix inverse (when the matrix is not singular) or pseudo-inverse will then be an inverse transformation; the inverse will exactly match the original data if the chosen sinusoids are mutually independent at the ...
This formula simplifies significantly when the upper right block matrix B is the zero matrix. This formulation is useful when the matrices A and D have relatively simple inverse formulas (or pseudo inverses in the case where the blocks are not all square. In this special case, the block matrix inversion formula stated in full generality above ...
In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of ...
The uniroot function implements the algorithm in R (software). The fzero function implements the algorithm in MATLAB. The Boost (C++ libraries) implements two algorithms based on Brent's method in C++ in the Math toolkit: Function minimization at minima.hpp with an example locating function minima.
The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's method. In particular, if either exp {\displaystyle \exp } or log {\displaystyle \log } in the complex domain can be computed with some complexity, then that complexity is ...