Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis
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Publication:2198193
DOI10.1007/s10092-020-00369-3OpenAlexW3048868576MaRDI QIDQ2198193
Mariarosa Mazza, Lidia Aceto, Stefano Serra Capizzano
Publication date: 9 September 2020
Published in: Calcolo (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10092-020-00369-3
spectral analysisToeplitz matricesmatrix transfer techniqueRiesz fractional derivative operatorGLT theory
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of matrix norms, conditioning, scaling (65F35) Linear operator approximation theory (47A58) Fractional ordinary differential equations (34A08) Toeplitz, Cauchy, and related matrices (15B05) Numerical computation of matrix exponential and similar matrix functions (65F60)
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Cites Work
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- A semi-alternating direction method for a 2-D fractional Fitzhugh-Nagumo monodomain model on an approximate irregular domain
- On the spectrum of stiffness matrices arising from isogeometric analysis
- A circulant preconditioner for fractional diffusion equations
- Multigrid method for fractional diffusion equations
- Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
- Ten equivalent definitions of the fractional Laplace operator
- Spectral analysis and structure preserving preconditioners for fractional diffusion equations
- Riesz potential operators and inverses via fractional centred derivatives
- Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
- Introduction to large truncated Toeplitz matrices
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- On the condition numbers of large semi-definite Toeplitz matrices
- On the extreme eigenvalues of Hermitian (block) Toeplitz matrices
- Efficient implementation of rational approximations to fractional differential operators
- Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations
- A unifying approach to some old and new theorems on distribution and clustering
- Fractional diffusion on bounded domains
- Rational Krylov methods for functions of matrices with applications to fractional partial differential equations
- Comparison analysis of two numerical methods for fractional diffusion problems based on the best rational approximations of \(t^\gamma\) on \([0, 1\)]
- Block generalized locally Toeplitz sequences: theory and applications in the unidimensional case
- Block generalized locally Toeplitz sequences: from the theory to the applications
- Rational approximations to fractional powers of self-adjoint positive operators
- Rational Approximation to the Fractional Laplacian Operator in Reaction-Diffusion Problems
- Generalized Locally Toeplitz Sequences: Theory and Applications
- Discretized Fractional Calculus
- Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
- Fractional Central Differences and Derivatives
- Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
- Asymptotic Results on the Spectra of Block Toeplitz Preconditioned Matrices
- Distribution of eigenvalues and singular values of Toeplitz matrices under weakened conditions on the generating function
- Are the eigenvalues of the B‐spline isogeometric analysis approximation of −Δu = λu known in almost closed form?
- A note on the spectral distribution of toeplitz matrices
- Generalized Locally Toeplitz Sequences: Theory and Applications
- Numerical approximation of fractional powers of elliptic operators
- Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations
