A New Method for TSVD Regularization Truncated Parameter Selection

• Published in: Mathematical problems in engineering Vol. 2013; no. 2013; pp. 1 - 9
• Main Authors: Tong, Yude, Xiang, Caibing, Bian, Shaofeng, Wu, Zemin
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2013; Hindawi Limited
• Subjects: Applied mathematics; Computational efficiency; Computer simulation; Decomposition; Engineering; Geodetics; Ill posed problems; Mathematical analysis; Mathematical models; Mathematical problems; Matrix methods; Mean square values; Optimization; Regularization; Simulation; Singular value decomposition
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2013/161834

The truncated singular value decomposition (TSVD) regularization applied in ill-posed problem is studied. Through mathematical analysis, a new method for truncated parameter selection which is applied in TSVD regularization is proposed. In the new method, all the local optimal truncated parameters are selected first by taking into account the interval estimation of the observation noises; then the optimal truncated parameter is selected from the local optimal ones. While comparing the new method with the traditional generalized cross-validation (GCV) and L curve methods, a random ill-posed matrices simulation approach is developed in order to make the comparison as statistically meaningful as possible. Simulation experiments have shown that the solutions applied with the new method have the smallest mean square errors, and the computational cost of the new algorithm is the least.