TY - BOOK

T1 - Combining approximate solutions for linear discrete ill-posed problems

AU - Hochstenbach, M.E.

AU - Reichel, L.

PY - 2011

Y1 - 2011

N2 - Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the singular value decomposition is available. This paper proposes to compute several approximate solutions by standard methods and then extract a new candidate solution from the linear subspace spanned by the available approximate solutions. We also describe how the method may be used for large-scale problems.
Key words: Ill-posed problem, linear combination, solution norm constraint, TSVD, Tikhonov regularization, discrepancy principle.

AB - Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the singular value decomposition is available. This paper proposes to compute several approximate solutions by standard methods and then extract a new candidate solution from the linear subspace spanned by the available approximate solutions. We also describe how the method may be used for large-scale problems.
Key words: Ill-posed problem, linear combination, solution norm constraint, TSVD, Tikhonov regularization, discrepancy principle.

M3 - Report

T3 - CASA-report

BT - Combining approximate solutions for linear discrete ill-posed problems

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -