Fast Structured Direct Spectral Methods for Differential Equations with Variable Coefficients, I. The One-Dimensional Case
DOI10.1137/140986815zbMath1330.65124OpenAlexW2229505215MaRDI QIDQ3460272
Jian-Lin Xia, Yingwei Wang, Jie Shen
Publication date: 7 January 2016
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/140986815
spectral methodlinear complexitymatrix factorizationnumerical teststructured matrixlow-rank propertymatrix-free direct solver
Nonlinear ordinary differential equations and systems (34A34) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Complexity and performance of numerical algorithms (65Y20) Direct numerical methods for linear systems and matrix inversion (65F05)
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Cites Work
- Unnamed Item
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- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- A fast direct solver for elliptic problems on general meshes in 2D
- Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications
- Fast construction of hierarchical matrix representation from matrix-vector multiplication
- A fast direct solver for a class of elliptic partial differential equations
- An adaptive fast direct solver for boundary integral equations in two dimensions
- A fast randomized algorithm for the approximation of matrices
- Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
- Spectral methods for problems in complex geometries
- Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients
- A fast direct solver for boundary integral equations in two dimensions
- Preconditioned minimal residual methods for Chebyshev spectral calculations
- Superfast Divide-and-Conquer Method and Perturbation Analysis for Structured Eigenvalue Solutions
- A Fast and Well-Conditioned Spectral Method
- A Well-Conditioned Collocation Method Using a Pseudospectral Integration Matrix
- Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Equations II. Unbounded Domains
- On the Complexity of Some Hierarchical Structured Matrix Algorithms
- A Fast Randomized Eigensolver with Structured LDL Factorization Update
- Spectral Methods
- On the Numerical Rank of the Off-Diagonal Blocks of Schur Complements of Discretized Elliptic PDEs
- Fast algorithms for hierarchically semiseparable matrices
- Superfast Multifrontal Method for Large Structured Linear Systems of Equations
- Fast Fourier Transforms for Nonequispaced Data
- Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials
- Efficient inversion of the Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients
- A Superfast Structured Solver for Toeplitz Linear Systems via Randomized Sampling
- Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems
- Preconditioning Chebyshev Spectral Collocation Method for Elliptic Partial Differential Equations
- A Fast $ULV$ Decomposition Solver for Hierarchically Semiseparable Representations
- An Algorithm for the Machine Calculation of Complex Fourier Series
- Sparse Spectral Approximations of High-Dimensional Problems Based on Hyperbolic Cross
- Spectral Methods
- A bibliography on semiseparable matrices
- A fast algorithm for particle simulations