Maximal perturbation bound for perturbed polynomials with roots in the left-sector

1994 ◽  
Vol 41 (4) ◽  
pp. 281-285 ◽  
Author(s):  
Y.C. Soh ◽  
L. Xie ◽  
Y.K. Foo
Keyword(s):  
Perturbation Bound ◽  
Perturbed Polynomials

scholarly journals Sensitivity Analysis of the Matrix Equation from Interpolation Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jing Li ◽  
Yuhai Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Approximate Solution ◽  
Matrix Equation ◽  
Nonlinear Matrix Equation ◽  
Backward Error ◽  
Perturbation Bound ◽  
Interpolation Problems ◽  
The Matrix ◽  
Nonlinear Matrix ◽  
Theoretical Results

This paper studies the sensitivity analysis of a nonlinear matrix equation connected to interpolation problems. The backward error estimates of an approximate solution to the equation are derived. A residual bound of an approximate solution to the equation is obtained. A perturbation bound for the unique solution to the equation is evaluated. This perturbation bound is independent of the exact solution of this equation. The theoretical results are illustrated by numerical examples.

scholarly journals The Perturbation Bound for the Spectral Radius of a Nonnegative Tensor

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wen Li ◽  
Michael K. Ng
Keyword(s):  
Spectral Radius ◽  
Perturbation Analysis ◽  
Absolute Difference ◽  
Nonnegative Tensor ◽  
Backward Error ◽  
Perturbation Bound ◽  
Error Matrix ◽  
Largest Eigenvalue ◽  
The Stability ◽  
The Largest Eigenvalue

We study the perturbation bound for the spectral radius of an mth-order n-dimensional nonnegative tensor A. The main contribution of this paper is to show that when A is perturbed to a nonnegative tensor A~ by ΔA, the absolute difference between the spectral radii of A and A~ is bounded by the largest magnitude of the ratio of the ith component of ΔAxm-1 and the ith component xm-1, where x is an eigenvector associated with the largest eigenvalue of A in magnitude and its entries are positive. We further derive the bound in terms of the entries of A only when x is not known in advance. Based on the perturbation analysis, we make use of the NQZ algorithm to estimate the spectral radius of a nonnegative tensor in general. On the other hand, we study the backward error matrix ΔA and obtain its smallest error bound for its perturbed largest eigenvalue and associated eigenvector of an irreducible nonnegative tensor. Based on the backward error analysis, we can estimate the stability of computation of the largest eigenvalue of an irreducible nonnegative tensor by the NQZ algorithm. Numerical examples are presented to illustrate the theoretical results of our perturbation analysis.

Stability of perturbed polynomials based on the argument principle and Nyquist criterion

1989 ◽  
Vol 50 (1) ◽  
pp. 55-63 ◽  
Author(s):  
S. H. LIN ◽  
I. K. FONG ◽  
Y. T. JUANG ◽  
T. S. KUO ◽  
C. F. HSU
Keyword(s):  
Argument Principle ◽  
Nyquist Criterion ◽  
Perturbed Polynomials

scholarly journals Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Huiming Duan ◽  
Kailiang Shao ◽  
Xinping Xiao ◽  
Jinwei Yang
Keyword(s):  
Fractional Order ◽  
Estimation Method ◽  
Original Data ◽  
Grey Model ◽  
Prediction Errors ◽  
Matrix Perturbation ◽  
Perturbation Bound ◽  
Grey Forecasting ◽  
The Matrix ◽  
The Stability

The grey forecasting model has been successfully applied in numerous fields since it was proposed. The nonhomogeneous discrete grey model (NDGM) was approximately constructed based on the nonhomogeneous index trend; it increased the applicability of discrete grey model. However, the NDGM required accurate data and better effect when the original data did not meet the conditions and fitting and prediction errors were larger. For this, the NDGM with the fractional order accumulating operator (abbreviated as NDGMp/q) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGMp/q and the NDGMp/q can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGMp/q was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGMp/q and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGMp/q was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.

scholarly journals Perturbation Bound for the Drazin Inverse of the Matrix-Value Function

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Yonghui Qin ◽  
Zhenshu Xie ◽  
Xiaoji Liu
Keyword(s):  
Perturbation Analysis ◽  
Upper Bound ◽  
Value Function ◽  
Drazin Inverse ◽  
Matrix Equations ◽  
Perturbation Bound ◽  
The Matrix

The perturbation analysis of the differential for the Drazin inverse of the matrix-value function A(t)∈Cn×n is investigated. An upper bound of the Drazin inverse and its differential is also considered. Applications to the perturbation bound for the solution of the matrix-value function coefficients some matrix equations are given.

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