On computing generalized inverse systems using matrix pencil methods
نویسنده
چکیده
We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state space representation. We put a particular emphasis on two classes of inverses: the week generalized inverse and the MoorePenrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil to appropriate Kronecker-like forms.
منابع مشابه
Computing Generalized Inverse Systems Using Matrix Pencil Methods
We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the MoorePenrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computati...
متن کاملEla the Drazin Inverse through the Matrix Pencil Approach and Its Application to the Study of Generalized Linear Systems with Rectangular or Square Coefficient Matrices∗
In several applications, e.g., in control and systems modeling theory, Drazin inverses and matrix pencil methods for the study of generalized (descriptor) linear systems are used extensively. In this paper, a relation between the Drazin inverse and the Kronecker canonical form of rectangular pencils is derived and fully investigated. Moreover, the relation between the Drazin inverse and the Wei...
متن کاملOn generalized inverses of singular matrix pencils
Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate s...
متن کاملInverse scattering problem for the Impulsive Schrodinger equation with a polynomial spectral dependence in the potential
In the present work, under some di¤erentiability conditions on the potential functions , we rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...
متن کاملSOLVING FUZZY LINEAR SYSTEMS BY USING THE SCHUR COMPLEMENT WHEN COEFFICIENT MATRIX IS AN M-MATRIX
This paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp M-matrix. Thefuzzy linear system (FLS) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. However, solving this crisp system isdifficult for large n because of dimensionality problems . It is shown that thisdifficulty may be avoide...
متن کامل