A truncated projected SVD method for linear discrete ill-posed problems

Truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems. However, since the singular value decomposition of the matrix is independent of the right-hand side, there are linear discrete ill-posed problems for which this method fails to yield an accurate approximate solution. This paper describes a new approach to incorporating knowledge about properties of the desired solution into the solution process through an initial projection of the linear discrete ill-posed problem. The projected problem is solved by truncated singular value decomposition. Computed examples illustrate that suitably chosen projections can enhance the accuracy of the computed solution. Key words. ill-posed problem, inverse problem, decomposition, svd, tsvd

• Type: Journal
• Year: 2006
• Where: NA
• Authors: Serena Morigi, Lothar Reichel, Fiorella Sgallari
• Keywords: Discrete Ill-posed Problem, Linear Discrete, NA 2006, Singular Value Decomposition