in this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. we then define products of $fs$-matrices andstudy their properties. we finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.

\Numerical inverting of matrices of high order", Bull. Amer. 18 Rounding errors do grow rapidly with the problem size n. The nal columns in the table give averages and maxima of`relative errors' jb RBT i ? b i j j j b RBT j j 1 where the b i values are either the computed solution from LINPACK, or the exact solution. For poorly-conditioned problems the RBT has large roundoo errors, which are so...

Structured real canonical forms for matrices in Rn×n that are symmetric or skewsymmetric about the anti-diagonal as well as the main diagonal are presented, and Jacobi algorithms for solving the complete eigenproblem for three of these four classes of matrices are developed. Based on the direct solution of 4 × 4 subproblems constructed via quaternions, the algorithms calculate structured orthog...

The Viewing Graph [1] represents several views linked by the corresponding fundamental matrices, estimated pairwise. Given a Viewing Graph, the tuples of consistent camera matrices form a family that we call the Solution Set. This paper provides a theoretical framework that formalizes different properties of the topology, linear solvability and number of solutions of multi-camera systems. We sy...

Structured real canonical forms for matrices in Rn×n that are symmetric or skew-symmetric about the anti-diagonal as well as the main diagonal are presented, and Jacobi algorithms for solving the complete eigenproblem for three of these four classes of matrices are developed. Based on the direct solution of 4× 4 subproblems constructed via quaternions, the algorithms calculate structured orthog...

In this paper we employ the Rosenbrock system matrix pencil for the computation of output-nulling subspaces of linear time-invariant systems which appear in the solution of a large number of control and estimation problems. We also consider the problem of finding friends of these output-nulling subspaces, i.e., the feedback matrices that render such subspaces invariant with respect to the close...

When the heat equation and wave equation are approximated by ut = −Ku and utt = −Ku (discrete in space), the solution operators involve e−Kt, √K, cos(√Kt), and sinc( √ Kt). We compute these four matrices and find accurate approximations with a variety of boundary conditions. The second difference matrix K is Toeplitz (shift-invariant) for Dirichlet boundary conditions, but we show why e−Kt also...

Lagrangian invariant subspaces for symplectic matrices play an important role in the numerical solution of discrete time, robust and optimal control problems. The sensitivity (perturbation) analysis of these subspaces, however, is a difficult problem, in particular, when the eigenvalues are on or close to some critical regions in the complex plane, such as the unit circle. We present a detailed...

A novel, transfer-function solution of the Kalman-Bucy time-invariant filtering problem is presented. It is assumed that both message model and noise intensities are time invariant and that the mixture of message and noise has been observed over an infinite interval. This transfer-function approach is based on matrix fractions and spectral factorization of polynomial matrices. It offers an inte...

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...