Convergence of block two-stage iterative methods for symmetric positive definite systems

2001 ◽  
Vol 90 (1) ◽  
pp. 47-63 ◽  
Author(s):  
Zhi-Hao Cao
Keyword(s):  
Iterative Methods ◽  
Positive Definite ◽  
Two Stage ◽  
Symmetric Positive Definite

Further Results on Iterative Approaches to the Determination of the Response of Nonclassically Damped Systems

1993 ◽  
Vol 60 (1) ◽  
pp. 235-239 ◽  
Author(s):  
Firdaus E. Udwadia
Keyword(s):  
Rate Of Convergence ◽  
Iterative Methods ◽  
Dynamic Systems ◽  
Positive Definite ◽  
Asymptotic Convergence ◽  
Iterative Schemes ◽  
Symmetric Positive Definite ◽  
Damping Matrix ◽  
Damped Systems

Iterative schemes for obtaining the response of nonclassically damped dynamic systems have been shown to converge when the damping matrix possesses certain specific characteristics. This paper extends those previous results which pertain to symmetric, positive-definite damping matrices. The paper considers a more general decomposition of the damping matrix, and extends the applicability of these iterative methods to all positive definite, symmetric damping matrices. This decomposition is governed by a parameter α. Conditions on α under which convergence is guaranteed are provided. Estimates of a which yield the fastest asymptotic convergence as well as estimates of the value of this asymptotic rate of convergence are also provided.

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