QR decomposition of almost strictly sign regular matrices

Depth of almost strictly sign regular matrices

“…So, NE transforms a nonsingular matrix into an upper triangular matrix. More results about NE and SR matrices can be seen in previous studies 9–14 and Alonso et al 15…”

“…So, NE transforms a nonsingular matrix into an upper triangular matrix. More results about NE and SR matrices can be seen in previous studies [9][10][11][12][13][14] and Alonso et al 15 In this paper, we introduce the concept of depth of an ASSR matrix. At the end of Section 4, we see that strictly M-banded ASSR matrices (see Alonso et al 16 ) are included in the class of ASSR matrices with depth n − M. We also see in Section 4 that the use of the depth of an ASSR matrix allows us to simplify the algorithms of Alonso et al 7 and to reduce their computational costs.…”

Almost strictly sign regular rectangular matrices

“…An important subclass of sign regular matrices is the class of almost strictly sign regular matrices, which present a special zero pattern and whose nontrivial minors are nonzero. Some properties of square almost strictly sign regular matrices have been studied (see, for instance, [2][3][4][5]).…”

Effective Methods of QR-Decompositions of Square Complex Matrices by Fast Discrete Signal-Induced Heap Transforms

“…The QR-decomposition, or factorization of a non-singular matrix = A QR into Advances in Linear Algebra & Matrix Theory a unitary matrix Q and an upper triangular matrix R, as well as the factorization = A QL with a low triangular matrix L are powerful tools for solving linear systems of equations = y Ax in many applications in computing and data analysis [1]- [7]. Here, the matrix A is a real or complex non-singular matrix.…”