A note on harmonic Ritz values and their reciprocals

2009 ◽  
Vol 17 (1) ◽  
pp. 97-108 ◽  
Author(s):  
Christof Vömel
Keyword(s):  
Ritz Values ◽  
Harmonic Ritz Values

scholarly journals Majorization Bounds for Ritz Values of Self-Adjoint Matrices

2020 ◽  
Vol 41 (2) ◽  
pp. 554-572
Author(s):  
Pedro G. Massey ◽  
Demetrio Stojanoff ◽  
Sebastian Zarate
Keyword(s):  
Ritz Values

scholarly journals A study of defect-based error estimates for the Krylov approximation of φ-functions

2021 ◽  
Author(s):  
Tobias Jawecki
Keyword(s):  
Error Estimates ◽  
Error Bounds ◽  
A Priori ◽  
Posteriori Error ◽  
Finite Precision ◽  
Ritz Values ◽  
A Posteriori Error Bounds ◽  
The Matrix ◽  
And Performance ◽  
Point Arithmetic

AbstractPrior recent work, devoted to the study of polynomial Krylov techniques for the approximation of the action of the matrix exponential etAv, is extended to the case of associated φ-functions (which occur within the class of exponential integrators). In particular, a posteriori error bounds and estimates, based on the notion of the defect (residual) of the Krylov approximation are considered. Computable error bounds and estimates are discussed and analyzed. This includes a new error bound which favorably compares to existing error bounds in specific cases. The accuracy of various error bounds is characterized in relation to corresponding Ritz values of A. Ritz values yield properties of the spectrum of A (specific properties are known a priori, e.g., for Hermitian or skew-Hermitian matrices) in relation to the actual starting vector v and can be computed. This gives theoretical results together with criteria to quantify the achieved accuracy on the fly. For other existing error estimates, the reliability and performance are studied by similar techniques. Effects of finite precision (floating point arithmetic) are also taken into account.

scholarly journals Ritz values of normal matrices and Ceva’s theorem

2013 ◽  
Vol 438 (11) ◽  
pp. 4114-4129 ◽  
Author(s):  
Russell Carden ◽  
Derek J. Hansen
Keyword(s):  
Ritz Values ◽  
Normal Matrices ◽  
Ceva’S Theorem
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