Inverse-free recursive multiresolution algorithms for a data approximation problem. (August 2016)

• Record Type: Journal Article
• Authors: Fortes, M.A.; Raydan, M.; Sajo-Castelli, A.M.
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 4(2016)
• Page Start: 1177
• Page End: 1187
• Publication Date: 2016-08
• Subjects: Inverse-free methods -- Multiresolution algorithms -- Data approximation -- Powell–Sabin element -- Noise reduction -- Energy localization; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.06.042
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We present inverse-free recursive multiresolution algorithms for data approximation problems based on energy functionals minimization. During the multiresolution process a linear system needs to be solved at each different resolution level, which can be solved with direct or iterative methods. Numerical results are reported, using the sparse Cholesky factorization, for two applications: one concerning the localization of regions in which the energy of a given surface is mostly concentrated, and another one regarding noise reduction of a given dataset. In addition, for large-scale data approximation problems that require a very fine resolution, we discuss the use of the Preconditioned Conjugate Gradient (PCG) iterative method coupled with a specialized monolithic preconditioner, for which one preconditioner is built for the highest resolution level and then the corresponding blocks of that preconditioner are used as preconditioners for the forthcoming lower levels.