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On the choice of subspace for iterative methods for linear discrete ill-posed problems

Daniela Calvetti, Bryan Lewis, Lothar Reichel (2001)

International Journal of Applied Mathematics and Computer Science

Many iterative methods for the solution of linear discrete ill-posed problems with a large matrix require the computed approximate solutions to be orthogonal to the null space of the matrix. We show that when the desired solution is not smooth, it may be possible to determine meaningful approximate solutions with less computational work by not imposing this orthogonality condition.

On the convergence theory of double K -weak splittings of type II

Vaibhav Shekhar, Nachiketa Mishra, Debasisha Mishra (2022)

Applications of Mathematics

Recently, Wang (2017) has introduced the K -nonnegative double splitting using the notion of matrices that leave a cone K n invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for K -weak regular and K -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes...

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