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Abstract
A matrix factorization technique called the NF (Nonsingular Factorization) algorithm is introduced. It has the following properties with respect to computing the matrix-vector product MX: (i) if M is an (n × n) Kronecker matrix, then the total number of multiplications followed by additions, (denoted by ∑), is such that : (ii)
if M is an (m × n) non-Kronecker matrix. The case
implies that no savings in arithmetic operation are realized.
The NF algorithm provides a means of readily obtaining factorizations associated with Kronecker matrices. In addition, it provides a unified approach for seeking factorizations of a class of non-Kronecker matrices (i.e., transformations) that are used in signal processing applications. In the past, the factorizations associated with such matrices have been sought using ad hoc techniques.