Tridiagonal systems play a fundamental role in matrix computation. In particular, in recent years parallel algorithms for the solution of tridiagonal systems have been developed. Among these, the cyclic reduction algorithm is particularly interesting. Here the stability of the cyclic reduction method is studied under the assumption of diagonal dominance. A backward error analysis is made, yield...

In this tutorial, we will continue the discussion, started in the tutorial 4, about the derivation of the fundamental solutions. In the former tutorial, we presented techniques for setting up the fundamental solution for simple and compound operators. Herein, we will discuss the use of operator decoupling technique to breakdown matrix operators to simple or compound scalar ones. This method is ...

The estimation of the fundamental matrix from a set of corresponding points is a relevant topic in epipolar stereo geometry [2]. Due to the high amount of outliers between the matches, RANSAC-based approaches [1] have been used to obtain the fundamental matrix. We introduce a new normalized epipolar error measure which takes into account the shape of the features used as matches [3] and does no...

lim t→s+ Γij(t, x, s, ·) = δijδx(·), Γij(·, ·, s, y) = 0 on ∂U = R × ∂Ω, where δij is the Kronecker delta symbol, δ(s,y)(·, ·) and δx(·) are Dirac delta functions. In particular, when U = R, the Green’s matrix (or Green’s function) is called the fundamental matrix (or fundamental solution). We prove that if weak solutions of (P) satisfy an interior Hölder continuity estimate (see Section 2.5 fo...

In the tutorial 3, we presented other examples on the derivation of the boundary integral equation in the direct form. Mainly, elasticity and plate in bending problems were discussed. In this tutorial, we will discuss the definitions and the methods of derivation of fundamental solutions. The use of such solution within the boundary element method was discussed in the former tutorial. A table p...

In this paper, an iterative method is proposed for solving the matrix inverse problem $AX=B$ for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix $A_0$, a solution $A^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of...

Fuzzy liner systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of inconsistent fuzzy matrix equation. Also some numerical examples are considered.  

Multiplicative preconditioning is a popular SVD-based techniques for the solution of linear systems of equations, but our SVD-free additive preconditioners are more readily available and better preserve matrix structure. We combine additive preconditioning with aggregation and other relevant techniques to facilitate the solution of linear systems of equations and some other fundamental matrix c...

Multiplicative preconditioning is a popular SVD-based techniques for the solution of linear systems of equations. Our novel SVD-free additive preconditioners are more readily available and better preserve matrix structure. We study their generation and their affect on conditioning of the input matrix. In other papers we combine additive preconditioning with aggregation and other relevant techni...

in the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(p,q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}a_{l}xb_{l}+overset{v} ‎{underset{s=1}{sum}}c_{s}widetilde{x}d_{s}=f$‎. ‎by this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎when the‎ ‎matrix equation is consistent over...