Positive Approximations of the Inverse of Fractional Powers of SPD M-Matrices

DOI10.1007/978-3-319-75169-6_8OpenAlexW2652027923MaRDI QIDQ4690906

Stanislav Harizanov, Svetozar Margenov

Publication date: 23 October 2018

Published in: Lecture Notes in Economics and Mathematical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.07620

zbMATH Keywords

best uniform rational approximationspositive approximations

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Numerical analysis (65-XX)

Related Items

Analysis of numerical methods for spectral fractional elliptic equations based on the best uniform rational approximation ⋮ Exponentially convergent trapezoidal rules to approximate fractional powers of operators ⋮ Neumann fractional diffusion problems: BURA solution methods and algorithms ⋮ Numerical solution of fractional diffusion-reaction problems based on BURA ⋮ Iterative low-rank approximation solvers for the extension method for fractional diffusion ⋮ A Gauss-Laguerre approach for the resolvent of fractional powers ⋮ A Gaussian method for the square root of accretive operators ⋮ Performance Analysis of MG Preconditioning on Intel Xeon Phi: Towards Scalability for Extreme Scale Problems with Fractional Laplacians ⋮ A fractional PDE model for turbulent velocity fields near solid walls

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Volume constrained 2-phase segmentation method utilizing a linear system solver based on the best uniform polynomial approximation of \(x^{- 1/2}\)
• Numerically solving an equation for fractional powers of elliptic operators
• Turbulence and diffusion. Scaling versus equations
• MIC(0) preconditioning of 3D FEM problems on unstructured grids: Conforming and non-conforming elements
• Robust algebraic multilevel methods and algorithms.
• The differential correction algorithm for generalized rational functions
• Rational approximation to \(x^\alpha\) on \([0,1\)]
• On square roots of M-matrices
• Chaos, fractional kinetics, and anomalous transport
• Reformulation of elasticity theory for discontinuities and long-range forces
• A numerical study of the homogeneous elliptic equation with fractional boundary conditions
• Rational approximation to \(|x|\)
• Nonlocal Operators with Applications to Image Processing
• The Fractional Laplacian
• The method of alternating projections and the method of subspace corrections in Hilbert space
• Optimal solvers for linear systems with fractional powers of sparse SPD matrices
• Numerical approximation of fractional powers of regularly accretive operators
• Best uniform rational approximation of 𝑥^{𝛼} on [0,1]
• Numerical approximation of fractional powers of elliptic operators
• Multilevel methods for nonuniformly elliptic operators and fractional diffusion