The algebraic eigenvalue problem
The algebraic eigenvalue problem
Fundamentals of matrix computations
Fundamentals of matrix computations
Backward error and condition of structured linear systems
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Structured Backward Error and Condition of Generalized Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
Eigenvalue patterned condition numbers: Toeplitz and Hankel cases
Journal of Computational and Applied Mathematics
| Hi-index | 7.30 |
We discuss questions of eigenvalue conditioning. We study in some depth relationships between the classical theory of conditioning and the theory of the zero-structured conditioning, and we derive from the existing theory formulae for the mathematical objects involved. Then an algorithm to compare the zero-structured individual condition numbers of a set of simple eigenvalues with the traditional ones is presented. Numerical tests are reported to highlight how the algorithm provides interesting information about eigenvalue sensitivity when the perturbations in the matrix have an arbitrarily assigned zero-structure. Patterned matrices (Toeplitz and Hankel) will be investigated in a forthcoming paper (Eigenvalue patterned condition numbers: Toeplitz and Hankel cases, Tech. Rep. 3, Mathematics Department, University of Rome 'La Sapienza', 2005.).