scholarly journals Effective Condition Number Bounds for Convex Regularization

2020 ◽  
Vol 66 (4) ◽  
pp. 2501-2516
Author(s):  
Dennis Amelunxen ◽  
Martin Lotz ◽  
Jake Walvin
Keyword(s):  
Condition Number ◽  
Effective Condition Number ◽  
Convex Regularization ◽  
Effective Condition

scholarly journals Analysis of the Boundary Knot Method for 3D Helmholtz-Type Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
F. Z. Wang ◽  
K. H. Zheng
Keyword(s):  
Boundary Conditions ◽  
Condition Number ◽  
Numerical Solutions ◽  
Type Equation ◽  
Coefficient Matrix ◽  
Stable Convergence ◽  
Convergence Results ◽  
Regularization Techniques ◽  
Effective Condition Number ◽  
Effective Condition

Numerical solutions of the boundary knot method (BKM) always perform oscillatory convergence when using a large number of boundary points in solving the Helmholtz-type problems. The main reason for this phenomenon may contribute to the severely ill-conditioned full coefficient matrix. In order to obtain admissible stable convergence results, regularization techniques and the effective condition number are employed in the process of simulating 3D Helmholtz-type problems. Numerical results are tested for the 3D Helmholtz-type equation with noisy and non-noisy boundary conditions. It is shown that the BKM in combination with the regularization techniques is able to produce stable numerical solutions.

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