Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective Methods of QR-Decompositions of Square Complex Matrices by
  Fast Discrete Signal-Induced Heap Transforms   The purpose of this work is to present an effective tool for computing
different QR-decompositions of a complex nonsingular square matrix. The concept
of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used.
This transform is fast, has a unique algorithm for any length of the input
vector/signal and can be used with different complex basic 2x2 transforms. The
DsiHT zeroes all components of the input signal while moving or heaping the
energy of the signal into one component, such as the first. We describe three
different types of QR-decompositions that use the basic transforms with the T,
G, and M-type complex matrices we introduce, and also without matrices, but
using analytical formulas. We also present the mixed QR-decomposition, when
different type DsiHTs are used at different stages of the algorithm. The number
of such decompositions is greater than 3^((N-1)), for an NxN complex matrix.
Examples of the QR-decomposition are described in detail for the 4x4 and 6x6
complex matrices and compared with the known method of Householder transforms.
The precision of the QR-decompositions of NxN matrices, when N are 6, 13, 17,
19, 21, 40, 64, 100, 128, 201, 256, and 400 is also compared. The MATLAB-based
scripts of the codes for QR-decompositions by the described DsiHTs are given.

21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph