We propose a new inertia-revealing factorization for sparse matrices. The factorization scheme and the method for extracting the inertia from it were proposed in the 1960s for dense, banded, or tridiagonal matrices, but they have been abandoned in favor of faster methods. We show that this scheme can be applied to any sparse matrix and that the fill in the factorization is bounded by the fill i...

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass respectively where the former is a necessary condition for the latter. Recently applications have arisen where asymptotic stability is too weak and stabi...

We propose a new pivot selection technique for symmetric indefinite factorization of sparse matrices. Such factorization should maintain both sparsity and numerical stability of the factors, both of which depend solely on the choices of the pivots. Our method is based on the minimum degree algorithm and also considers the stability of the factors at the same time. Our experiments show that our ...

Non-standard backward heat conduction problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In this paper, we propose a regularization strategy-quasi-reversibility method to analysis the stability of the problem. Meanwhile, we investigate the roles of regularization parameter in this method. Numerical result shows that our algorithm is effe...

Abslrocr -Suppose that a rational function Z ( s ) is defined by a Laurent .series, the coefficients of which are known. Several criteria are given in terms of these coefficients (the Markov parameters of Z(s)) to ensure that Re Z ( j w ) > 0 for all red w. The criteria are defined by using a Cauchy index formulation of the ratio of two rational functions, and they are of three types-involving ...

this paper proposes a new method of gain scheduling control design for a nonlinear system which is described as linear parameter varying form. a performance measure based on linear matrix inequality is introduced. to consider stability and performance measures in design process, the h∞ loop-shaping method is used to design the local controllers, which can be described as state feedback observer...

in this study, a robust controller is designed for fuzzy network control systems (ncss) using the static output feedback. delay and data packet dropout affect on the stability of network control systems, and therefore, the asymptotic stability condition is established considering delay and data packet dropout. delay is time-varying while the lower and upper bounds for delay is defined, and the ...

A general framework for the regularization of constrained PDEs, also called operator DAEs, is presented. The given procedure works for semi-explicit operator DAEs of first order which includes the Navier-Stokes and other flow equations. This reformulation is a regularization in the sense that a semi-discretization in space leads to a DAE of lower index, i.e., of differentiation index 1 instead ...

We present a fast and numerically stable algorithm for computing the eigendecom-position of a symmetric block diagonal plus semiseparable matrix. We report numerical experiments that indicate that our algorithm is signiicantly faster than the standard method which treats the given matrix as a general symmetric dense matrix.