Back to Search
Start Over
Estimation of the bilinear form y⁎f(A)x for Hermitian matrices.
- Source :
-
Linear Algebra & its Applications . Aug2016, Vol. 502, p140-158. 19p. - Publication Year :
- 2016
-
Abstract
- For a Hermitian matrix A ∈ C p × p , given vectors x , y ∈ C p and for suitable functions f , the bilinear form y ⁎ f ( A ) x is estimated by extending the extrapolation method proposed by C. Brezinski in 1999. Families of one term and two term estimates e f , ν , ν ∈ C and e ˆ f , n , k , n , k ∈ Z , respectively, are derived by extrapolation of the moments of the matrix A . For the positive definite case, bounds for the optimal value of ν , which leads to an efficient one term estimate in only one matrix vector product, are derived. For f ( A ) = A − 1 , a formula approximating this optimal value of ν is specified. Numerical results for several matrix functions and comparisons are provided to demonstrate the effectiveness of the extrapolation method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 502
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 114905696
- Full Text :
- https://doi.org/10.1016/j.laa.2015.08.033