Matrix pencil - Wikipedia
In linear algebra, a matrix pencil is a matrix-valued polynomial function defined on a field, usually the real or complex numbers.
Matrix pencils: Theory, applications, and numerical methods
This paper surveys nearly all of the publications that have appeared in the last twenty years on the theory of and numerical methods for linear pencils.
The theory of matrix pencils (especially linear pencils) occupies an increasingly important place in contemporary linear algebra and its applications.
A matrix pencil of degree n is defined as an nth degree polynomial with matrix-coefficients as follows, 1 ( ) 11... nn λλ λ λAnn. AA. −. Γ= + ++ + −. A. where λ∈. C , nn,1,2,..., Ai Ci ∈= ×. n, and . 0. A. n. ≠, a zero matrix. A particular case known as linear matrix pencil, denoted as , has been studied extensively with ...
Generalized pencil-of-function method - Wikipedia
Generalized pencil-of-function method (GPOF), also known as matrix pencil method, is a signal processing technique for estimating a signal or extracting information with complex exponentials. Being similar to Prony and original pencil-of-function methods, it is generally preferred to those for its robustness and computational efficiency.
DIFFERENTIAL/ALGEBRAIC SYSTEMS AND MATRIX PENCILS* C. W. Gear Department of Computer Science, University of Illinois at Urbana-Champaign L. R. Petzold Sandia National Laboratories, Livermore Abstract In this paper we study the numerical solution of the differential/algebraic systems F(t, y, y') = O. Many of these systems can be solved ...
Singular Matrix Pencils and the QZ Algorithm » Cleve’s Corner: …
Jan 5, 2023 · And, the QZ-algorithm can help detect and analyze exceptional situaions known as singular pencils. If A and B are two square matrices, the linear matrix pencil is the matrix-valued function. A - λB. A pencil is regular if there is at least one value of λ for which A - λB if not singular.
In Section 2 the matrix pencil associated with the classical complex exponential fitting or sparse interpolation problem is summarized and the concepts of dilation and translation are introduced to obtain matrix pencils at diferent scales.
Hamiltonian matrix Has a matrix pencil J JH, i.e., a pencil where one of the matrices is skew Hermitian and the other is Hermitian. Using congruence transformations UH( J JH)U, we obtain a canonical form via classical results for such pencils, see e.g., [22, 23].
Matrix pencils: Theory, applications, and numerical methods
Apr 1, 1993 · The matrix pencil method (MPM) is tested as an approach to quantitatively process multiexponential low-field nuclear magnetic resonance T1 relaxometry data.