Incomplete cross approximation in the mosaic-skeleton method
From MaRDI portal
Publication:1581115
DOI10.1007/s006070070031zbMath0964.65048OpenAlexW1969720662WikidataQ60060393 ScholiaQ60060393MaRDI QIDQ1581115
Publication date: 23 July 2001
Published in: Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s006070070031
algorithmvery large matricesmosaic-skeleton methodmatrix-vector multiplicationslow mosaic rankmosaic partitioning
Computational methods for sparse matrices (65F50) Direct numerical methods for linear systems and matrix inversion (65F05)
Related Items
Adaptive cross approximation for ill-posed problems, Efficient algorithms for CUR and interpolative matrix decompositions, A structured low-rank wavelet solver for the Ornstein-Zernike integral equation, Existence of $\mathcal {H}$-matrix approximants to the inverses of BEM matrices: The simple-layer operator, Aggregation in non-uniform systems with advection and localized source, A low-rank approach to the computation of path integrals, Computation of extreme eigenvalues in higher dimensions using block tensor train format, Mosaic-skeleton method as applied to the numerical solution of three-dimensional Dirichlet problems for the Helmholtz equation in integral form, A unifying approach to the construction of circulant preconditioners, The ACA-BEM approach with a binary-key mosaic partitioning for modelling multiple bubble dynamics, Matrix approximations and solvers using tensor products and non-standard wavelet transforms related to irregular grids, ℌ 2 $$\mathcal{H}^{2}$$ Matrix and Integral Equation for Electromagnetic Scattering by a Perfectly Conducting Object, Parallel implementation for some applications of integral equations method, Global and local optimization in identification of parabolic systems, Subset selection for matrices, Pseudo-skeleton approximations with better accuracy estimates, Low-rank approximation of integral operators by using the Green formula and quadrature, A tensor-train accelerated solver for integral equations in complex geometries, Optimal rank matrix algebras preconditioners, A randomized algorithm for the decomposition of matrices, Simpler is better: a comparative study of randomized pivoting algorithms for CUR and interpolative decompositions, HODLR2D: A New Class of Hierarchical Matrices, On the existence of mosaic-skeleton approximations for discrete analogues of integral operators, Adaptive cross approximation for Tikhonov regularization in general form, Study of performance of low-rank nonnegative tensor factorization methods, A probabilistic reduced basis method for parameter-dependent problems, HODLR\(d\)D: a new black-box fast algorithm for \(N\)-body problems in \(d\)-dimensions with guaranteed error bounds. Applications to integral equations and support vector machines, Gradient-type methods: a unified perspective in computer science and numerical analysis, On the application of Mosaic-Skeleton approximations of matrices in electrodynamics problems with impedance boundary conditions, Literature survey on low rank approximation of matrices, Solving the transport-coagulation problem in a two-dimensional spatial region, Global optimization based on TT-decomposition, Optimal CUR Matrix Decompositions, An efficient numerical method for a mathematical model of a transport of coagulating particles, Using the Tensor-Train Approach to Solve the Ground-State Eigenproblem for Hydrogen Molecules, Matrices with Hierarchical Low-Rank Structures, Parallel mosaic-skeleton algorithm for the numerical solution of a three-dimensional scalar scattering problem in integral form, Parallel cross interpolation for high-precision calculation of high-dimensional integrals, Mathematical modeling of the Wuhan COVID-2019 epidemic and inverse problems, Kronecker-product approximations for some function-related matrices., Quasioptimality of skeleton approximation of a matrix in the Chebyshev norm, Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy, A geometric mapping cross approximation method, Transformations of matrix structures work again, Approximate iterations for structured matrices, Hierarchical Kronecker tensor-product approximations, Nonnegative Tensor Train Factorizations and Some Applications, Low Rank Structures in Solving Electromagnetic Problems, Global Optimization Algorithms Using Tensor Trains, Regression-aware decompositions, Tensor Completion via Gaussian Process--Based Initialization, Adaptive directional compression of high-frequency Helmholtz boundary element matrices, Randomized algorithms for the low-rank approximation of matrices, Fast truncation of mode ranks for bilinear tensor operations, A fast randomized algorithm for the approximation of matrices, Tensor based approach to the numerical treatment of the parameter estimation problems in mathematical immunology, New accuracy estimates for pseudoskeleton approximations of matrices, A fast 3D dual boundary element method based on hierarchical matrices, Quasioptimality of maximum-volume cross interpolation of tensors, A note on tensor chain approximation, Fast low‐rank approximations of multidimensional integrals in ion‐atomic collisions modelling, Iterative representing set selection for nested cross approximation, Low-Rank Approximation of a Matrix: Novel Insights, New Progress, and Extensions, Adaptive recompression of \(\mathcal H\)-matrices for BEM, Generalizing the column-row matrix decomposition to multi-way arrays, Fast randomized matrix and tensor interpolative decomposition using countsketch, Solving a large dense linear system by adaptive cross approximation, Methods for nonnegative matrix factorization based on low-rank cross approximations, On the existence of a nearly optimal skeleton approximation of a matrix in the Frobenius norm, Tensor Algorithms for Advanced Sensitivity Metrics, Fast algorithms for spherical harmonic expansions. III, Approximation of integral operators by Green quadrature and nested cross approximation, TT-cross approximation for multidimensional arrays, Randomized interpolative decomposition of separated representations, A fast numerical method for the Cauchy problem for the Smoluchowski equation, Grid-based electronic structure calculations: the tensor decomposition approach, Evaluation of the Docking Algorithm Based on Tensor Train Global Pptimization, Tensor-train numerical integration of multivariate functions with singularities, Nonnegative tensor train factorization with DMRG technique, Cross approximation in tensor electron density computations, Hierarchical matrix approximation to Green's function via boundary concentrated FEM, Fast Low-Rank Kernel Matrix Factorization Using Skeletonized Interpolation, Scalable Matrix-Free Adaptive Product-Convolution Approximation for Locally Translation-Invariant Operators, Riemannian Optimization for High-Dimensional Tensor Completion, Parallel Randomized and Matrix-Free Direct Solvers for Large Structured Dense Linear Systems, Hierarchical algorithms on hierarchical architectures, Approximate solution of linear systems with Laplace-like operators via cross approximation in the frequency domain, Approximation of matrices with logarithmic number of parameters, Application of mosaic-skeleton approximations of matrices in the physical optics method for electromagnetic scattering problems, Tensor representation of non-linear models using cross approximations, Hybrid cross approximation of integral operators, Fast Multidimensional Convolution in Low-Rank Tensor Formats via Cross Approximation, Tensor properties of multilevel Toeplitz and related matrices, A literature survey of low-rank tensor approximation techniques, Solving linear systems using wavelet compression combined with Kronecker product approx\-i\-ma\-tion, Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices, Fast approximate computations with Cauchy matrices and polynomials