Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4628841 | Applied Mathematics and Computation | 2013 | 10 Pages |
Abstract
This paper concerns the partial derivatives of the eigen-triplet of the quadratic matrix polynomial Q(p,λ)=λ2M(p)+λC(p)+K(p), where M(p),C(p),K(p)âCnÃn are complex analytic matrix valued functions, pâCm is a complex parameter vector. First, the analyticity theorem for simple eigenvalues and the corresponding eigenvectors is given. Second, a new method is proposed to compute partial derivatives of the eigen-triplet. The derivatives of the eigen-triplet can be obtained by solving algebraic linear equations of order (n-1), where it only requires the information of the eigen-triplet whose partial derivatives are to be computed, and what is more important, the condition numbers of the coefficient matrices are “better” than those of the nonsingular coefficient matrices arisen in the bordered matrix method [1] and Nelson's method [5]. Numerical tests show the feasibility and efficiency of the new method. The results are better or at least comparable with current methods.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Xin Lu, Shu-fang Xu, Yun-feng Cai,