For an n × n tridiagonal matrix we exploit the structure of its QR factorization to devise two new algorithms for computing the 1-norm condition number in O(n) operations. The algorithms avoid underflow and overflow, and are simpler than existing algorithms since tests are not required for degenerate cases. An error analysis of the first algorithm is given, while the second algorithm is shown t...

This paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. This new algorithm ca...

To some extent, graph evolutionary mechanisms can be explained by its spectra. Here, we are interested in two graph operations, namely, motif (subgraph) doubling and attachment that are biologically relevant. We investigate how these two processes affect the spectrum of the normalized graph Laplacian. A high (algebraic) multiplicity of the eigenvalues 1, 1±0.5, 1± √ 0.5 and others has been obse...

Covering rough set theory provides an effective approach to dealing with uncertainty in data analysis. Knowledge acquisition is a main issue in covering rough set theory. However, the original rough set methods are still expensive for this issue in terms of time consumption. To further improvement, we propose fast approaches to knowledge acquisition in covering information systems by employing ...

GPU VSIPL is an implementation of the Vector Signal Image Processing Library (VSIPL) and provides a librarybased solution to developing GPU-accelerated numerical applications. GPU VSIPL now supports much of the VSIPL Core Profile as well as element-wise matrix operators corresponding to required vector operators. This is nearly a five-fold increase in function count since GPU VSIPL was first in...

In this paper, we consider the automatic performance tuning of dense vector and matrix-vector operations on GPUs. Such operations form the backbone of level 1 and level 2 routines in the Basic Linear Algebra Subroutines (BLAS) library and are therefore of great importance in many scientific applications. As examples, we develop single-precision CUDA kernels for the euclidian norm (SNRM2) and th...

This paper presents a new approach for large-deflection analysis of truss structures employing the Dynamic Relaxation method (DR). The typical formulation for DR has been established utilizing the finite difference technique which is categorized as an explicit method. The special characteristic of the explicit method is its simple algebraic relationships in comparison with complicated matrix op...

We present a new algorithm for reducing an arbitrary unitary matrix into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of quantum bits (i.e., a quantum computer). We report on a C++ program called “Qubiter” that implements our algorithm. Qubiter source code is publicly available.

In this paper we study fuzzy soft matrix based on reference function.Firstly, we define some new operations such as fuzzy soft complement matrix and trace of fuzzy soft matrix based on reference function.Then, we introduced some related properties, and some examples are given. Lastly, we define a new fuzzy soft matrix decision method based on reference function.