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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...
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...
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