Displaying similar documents to “Residual norm behavior for Hybrid LSQR regularization”

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

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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.

Numerical Treatment of a Time Dependent Inverse Problem in Photon Transport

Sandra Pieraccini, Riccardo Riganti, Aldo Belleni-Morante (2007)

Bollettino dell'Unione Matematica Italiana

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The time-dependent intensity of a UV -photon source, located inside an interstellar cloud, is determined by formulating and solving an inverse problem for the integro-differential transport equation of photons in a one-dimensional slab. Starting from a discretizazion of the direct problem, an iterative procedure is used to compute the values of the source intensity at increasing values of time, and it is applied in some numerical simulations, whose results are presented and discussed. ...

An improved nonmonotone adaptive trust region method

Yanqin Xue, Hongwei Liu, Zexian Liu (2019)

Applications of Mathematics

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Trust region methods are a class of effective iterative schemes in numerical optimization. In this paper, a new improved nonmonotone adaptive trust region method for solving unconstrained optimization problems is proposed. We construct an approximate model where the approximation to Hessian matrix is updated by the scaled memoryless BFGS update formula, and incorporate a nonmonotone technique with the new proposed adaptive trust region radius. The new ratio to adjusting the next trust...

New SOR-like methods for solving the Sylvester equation

Jakub Kierzkowski (2015)

Open Mathematics

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We present new iterative methods for solving the Sylvester equation belonging to the class of SOR-like methods, based on the SOR (Successive Over-Relaxation) method for solving linear systems. We discuss convergence characteristics of the methods. Numerical experimentation results are included, illustrating the theoretical results and some other noteworthy properties of the Methods.