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

100%

Calvetti D., Lewis B., Reichel L.

International Journal of Applied Mathematics and Computer Science

2001

tom 11

nr 5

1069-1092

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.

Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition

100%

Koko J.

International Journal of Applied Mathematics and Computer Science

2004

tom 14

nr 1

13-18

Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each step.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Calvetti D.

1 Koko J.

1 Lewis B.

1 Reichel L.

1 2004

1 2001

Wyniki wyszukiwania

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

Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition