A QR-Decomposition for Matrix Pencils
نویسنده
چکیده
This paper describes an eecient and numerically stable modiication of the QR decomposition for solving a parametric set of linear least squares problems with a parametric matrix A+B for several values of the parameter. The method is demonstrated on a typical application.
منابع مشابه
A generalized structured doubling algorithm for optimal control problems
We propose a generalization of the Structured Doubling Algorithm (SDA) to compute invariant subspaces of structured matrix pencils that arise in the context of solving linear quadratic optimal control problems. The new algorithm is designed to attain better accuracy when the classical Riccati equation approach for the solution of the optimal control problem is not well suited because the stable...
متن کاملStructured Backward Error Analysis of Linearized Structured Polynomial Eigenvalue Problems
We start by introducing a new class of structured matrix polynomials, namely, the class of MA-structured matrix polynomials, to provide a common framework for many classes of structured matrix polynomials that are important in applications: the classes of (skew-)symmetric, (anti-)palindromic, and alternating matrix polynomials. Then, we introduce the families of MAstructured strong block minima...
متن کاملNew Bases for Polynomial-Based Spaces
Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...
متن کاملThe Analysis and Comparison of Algorithm in QR Decomposition
QR decomposition of matrix is one of the important problems in the field of matrix theory. Besides, there are also so many extensive applications that using QR decomposition. Because of that, there are many researchers have been studying about algorithm for this decomposition. Two of those researchers are Feng Tianxiang and Liu Hongxia. In their paper, they proposed new algorithm to make QR dec...
متن کاملOptimal Scaling of Companion Pencils for the QZ-Algorithm∗†
Computing roots of a monic polynomial may be done by computing the eigenvalues of the corresponding companion matrix using for instance the well-known QR-algorithm. We know this algorithm to be backward stable since it computes exact eigenvalues of a slightly modified matrix. But it may yield very poor backward errors in the coefficients of the polynomial. In this paper we investigate what can ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999