Linear systems arising in interior methods for convex optimization: a symmetric formulation with bounded condition number

2021 ◽  
pp. 1-26
Author(s):  
Alexandre Ghannad ◽  
Dominique Orban ◽  
Michael A. Saunders
Keyword(s):  
Convex Optimization ◽  
Linear Systems ◽  
Condition Number ◽  
Interior Methods ◽  
Symmetric Formulation

scholarly journals Schwarz Methods for a Preconditioned WOPSIP Method for Elliptic Problems

2012 ◽  
Vol 12 (3) ◽  
pp. 241-272 ◽  
Author(s):  
Paola F. Antonietti ◽  
Blanca Ayuso de Dios ◽  
Susanne C. Brenner ◽  
Li-yeng Sung
Keyword(s):  
Boundary Value Problem ◽  
Linear Systems ◽  
Condition Number ◽  
Numerical Experiments ◽  
Boundary Value ◽  
Penalty Parameter ◽  
Systems Of Equations ◽  
Schwarz Methods ◽  
Interior Penalty ◽  
Linear Systems Of Equations

Abstract We propose and analyze several two-level non-overlapping Schwarz methods for a preconditioned weakly over-penalized symmetric interior penalty (WOPSIP) discretization of a second order boundary value problem. We show that the preconditioners are scalable and that the condition number of the resulting preconditioned linear systems of equations is independent of the penalty parameter and is of order H/h, where H and h represent the mesh sizes of the coarse and fine partitions, respectively. Numerical experiments that illustrate the performance of the proposed two-level Schwarz methods are also presented.

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