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Experiments with Krylov subspace methods on a massively parallel computer

Martin HankeMarlis HochbruckWilhelm Niethammer — 1993

Applications of Mathematics

In this note, we compare some Krylov subspace iterative methods on the MASPAR, a massively parallel computer with 16K processors. In particular, we apply these methods to solve large sparse nonsymmetric linear systems arising from elliptic partial differential equations. The methods under consideration include conjugate gradient type methods, semiiterative methods, and a hybrid variant. Our numerical results show that, on the MASPAR, one should compare iterative methods rather on the basis of total...

Regularization of nonlinear ill-posed problems by exponential integrators

Marlis HochbruckMichael HönigAlexander Ostermann — 2009

ESAIM: Mathematical Modelling and Numerical Analysis

The numerical solution of ill-posed problems requires suitable regularization techniques. One possible option is to consider time integration methods to solve the Showalter differential equation numerically. The stopping time of the numerical integrator corresponds to the regularization parameter. A number of well-known regularization methods such as the Landweber iteration or the Levenberg-Marquardt method can be interpreted as variants of the Euler method for solving the Showalter differential...

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