Preconditioned conjugate gradient method for finding minimal energy surfaces on Powell-Sabin triangulations

DOI10.1016/j.cam.2014.02.030zbMath1293.65034OpenAlexW2061903618MaRDI QIDQ396247

Mohammad Hasan, H. S. Yoon

Publication date: 8 August 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2014.02.030

zbMATH Keywords

preconditioningconjugate gradient methoddata approximationminimal energy surfacesPowell-Sabin element

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items (7)

Geometrical inverse matrix approximation for least-squares problems and acceleration strategies ⋮ Hole-filling techniques by using minimal energy surfaces ⋮ Sparse approximate solution of fitting surface to scattered points by MLASSO model ⋮ Relationship between quality of basis for surface approximation and the effect of applying preconditioning strategies to their resulting linear systems ⋮ Geometrical inverse preconditioning for symmetric positive definite matrices ⋮ Inverse-free recursive multiresolution algorithms for a data approximation problem ⋮ Fitting and filling of 3D datasets with volume constraints using radial basis functions under tension

Cites Work

• Minimal energy surfaces using parametric splines
• \(C^ r\)-finite elements of Powell-Sabin type on the three direction mesh
• Minimal energy \(C^r\)-surfaces on uniform Powell-Sabin-type meshes for noisy data
• Filling polygonal holes with minimal energy surfaces on Powell-Sabin type triangulations
• Approximation order of bivariate spline interpolation for arbitrary smoothness
• Scattered data interpolation using minimum energy Powell-Sabin elements and data dependent triangulations
• Matrix differential equations and inverse preconditioners
• Minimal energy \(C^r\)-surfaces on uniform Powell-Sabin type meshes. Estimation of the smoothing parameters
• Differential equations and solution of linear systems
• Practical Use of Polynomial Preconditionings for the Conjugate Gradient Method
• Error Bounds for Hermite Interpolation by Quadratic Splines on an  -Triangulation
• Piecewise Quadratic Approximations on Triangles
• Iterative Solution Methods
• An improved incomplete Cholesky factorization
• Matrix Preconditioning Techniques and Applications
• MODIFLED INCOMPLETE CHOLESKY FACTORIZATION PRECONDITIONERS FOR A SYMMETRIC POSITIVE DEFINITE MATRIX
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