08:30
Numerical Linear Algebra (Part 2)
Chair: Chandrasekhar Venkataraman
08:30
25 mins
|
CG variants for general-form regularization with an application to low-field MRI
Merel de Leeuw den Bouter, Martin van Gijzen, Rob Remis
Abstract: In an earlier paper, we generalized the CGME (Conjugate Gradient Minimal Error) algorithm to the L2-regularized weighted least-squares problem.
Here, we use this Generalized CGME method to reconstruct images from actual signals measured using a low-field MRI scanner. We analyze the convergence of both GCGME and the classical Generalized Conjugate Gradient Least Squares (GCGLS) method for the simple case when a Laplace operator is used as a regularizer and indicate when GCGME is to be preferred in terms of convergence speed.
We also consider a more complicated L1-penalty in a compressed sensing framework.
|
08:55
25 mins
|
Verified solutions of large sparse linear systems arising from 3D Poisson equation in HPC environments
Takeshi Ogita, Kengo Nakajima
Abstract: In this talk, we adapt a verification method to high-performance computing (HPC) environments. For this purpose, we modify several points in terms of both the quality of the verified error bounds and the speed of the verification process: we tighten the computed error bounds using the high-precision residual computation and speed up the verification process by reducing the memory access.
|
09:20
25 mins
|
A time-simultaneous multigrid method for parabolic evolution equations
Jonas Dünnebacke, Stefan Turek, Peter Zajac, Andriy Sokolov
Abstract: We present a time-simultaneous multigrid scheme for parabolic equations
that is motivated by blocking multiple time steps together. The resulting method is
closely related to multigrid waveform relaxation and is robust with respect to the
spatial and temporal grid size and the number of simultaneously computed time
steps. We give an intuitive understanding of the convergence behavior and briefly
discuss how the theory for multigrid waveform relaxation can be applied in some
special cases. Finally, some numerical results for linear and also nonlinear test cases
are shown.
|
|
