Sherman-Morrison-Woodbury-formula-based algorithms for the surface smoothing problem
type: Item
instance of: scholarly article
title: Sherman-Morrison-Woodbury-formula-based algorithms for the surface smoothing problem
zbMATH Open document ID: 0887.65012
DOI: 10.1016/S0024-3795(97)80366-7
author: Shang-Hong Lai
author: Baba C. Vemuri
published in: Linear Algebra and its Applications
publication date: 1998-05-25T00:00:00Z
review text: The purpose of the paper is to present a new and fast algorithm for solving the sparse- and dense-data surface smoothing problems using a membrane, thin-plate, or thin-plate membrane spline for data containing discontinuities. These problems are formulated as solutions to a Lyapunov matrix equation or a cascade of two Lyapunov matrix equations with an appropriate right-hand-side by using the Sherman-Morrison-Woodbury formula of matrix analysis. The efficiency of the algorithm is demonstrated through experiments on sparse-data surface smoothing. The numerical results are compared to the conjugate gradient algorithm and the hierarchical-basis preconditioned conjugate gradient algorithm.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 1076379
zbMATH Keywords: discontinuous data
zbMATH Keywords: algorithm
zbMATH Keywords: surface smoothing
zbMATH Keywords: thin-plate membrane spline
zbMATH Keywords: Lyapunov matrix equation
zbMATH Keywords: Sherman-Morrison-Woodbury formula
zbMATH Keywords: numerical results
zbMATH Keywords: hierarchical-basis preconditioned conjugate gradient algorithm
reviewed by: J. Illán
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1076379