This report presents a new analytic method for checking the Schur stability of interval polynomial matrix (polynomials whose coefficients are interval matrices). In the suggested method, the interval Markov matrices of the interval polynomial matrix are used to assess its stability. The validity of the suggested method is illustrated through numerical examples. The proposed technique is algebra...

We define strong regularity of a parametric interval matrix and give conditions that characterize it. The new conditions give a better estimation for regularity of a parametric matrix than the conditions used so far. Verifiable sufficient regularity conditions are also presented for parametric matrices. The new sufficient conditions motivate a generalization of Rump’s parametric fixed-point ite...

‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matr...

in this paper a guided tabu search (gts) is utilized for optimal nodal ordering of finite element models (fems) leading to small profile for the stiffness matrices of the models. the search strategy is accelerated and a graph-theoretical approach is used as guidance. the method is evaluated by minimization of graph matrices pattern equivalent to stiffness matrices of finite element models. comp...

By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations. Keywords—Interval arithmetic, Interval matrix, linear equations.

The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when dealing with interval matrices exponentiation: Indeed, the main problem will now be the dependency loss of the different occurrences of the variables due to int...

In this short note, we present a novel method for computing exact lower and upper bounds of a symmetric tridiagonal interval matrix. Compared to the known methods, our approach is fast, simple to present and to implement, and avoids any assumptions Our construction explicitly yields those matrices for which particular lower and upper bounds are attained.