Note on Finding an Optimal Deflation for Quadratic Matrix Polynomials
نویسندگان
چکیده
منابع مشابه
Triangularizing Quadratic Matrix Polynomials
We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal bloc...
متن کاملLinear quadratic optimal control, dissipativity, and para-Hermitian matrix polynomials
In this paper we will look at two results in which a special para-Hermitian matrix polynomial appears in linear quadratic systems theory. The first result constitutes the first step in a dissipativity check. The second result shows that dissipativity is equivalent to the solvability of the infinitehorizon linear quadratic optimal control problem and that its solutions are given by the behavior ...
متن کاملStrongly Damped Quadratic Matrix Polynomials
We study the eigenvalues and eigenspaces of the quadratic matrix polynomial Mλ + sDλ + K as s → ∞, where M and K are symmetric positive definite and D is symmetric positive semi-definite. The work is motivated by its application to modal analysis of finite element models with strong linear damping. Our results yield a mathematical explanation of why too strong damping may lead to practically un...
متن کاملAN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX
The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation...
متن کاملHaar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems
In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, Haar wavelets are applied for converting the TBVP, as a system of differential equations, in to a system of matrix algebraic equations...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: CSIAM Transactions on Applied Mathematics
سال: 2021
ISSN: 2708-0560,2708-0579
DOI: 10.4208/csiam-am.2021.nla.05