SIAM Journal on Scientific Computing
On randomized Lanczos algorithms
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
A Fourier-wavelet Monte Carlo method for fractal random fields
Journal of Computational Physics
Approximating matrix multiplication for pattern recognition tasks
Journal of Algorithms
Latent semantic indexing: a probabilistic analysis
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Pass efficient algorithms for approximating large matrices
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Spectral Partitioning with Indefinite Kernels Using the Nyström Extension
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
A Krylov Subspace Method for Covariance Approximation and Simulation of Random Processes and Fields
Multidimensional Systems and Signal Processing
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
Journal of Computer and System Sciences - Special issu on PODS 2001
Fast Monte-Carlo Algorithms for Approximate Matrix Multiplication
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Clustering Large Graphs via the Singular Value Decomposition
Machine Learning
Fast monte-carlo algorithms for finding low-rank approximations
Journal of the ACM (JACM)
Algorithms for Numerical Analysis in High Dimensions
SIAM Journal on Scientific Computing
Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication
SIAM Journal on Computing
Improved Approximation Algorithms for Large Matrices via Random Projections
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fast computation of low-rank matrix approximations
Journal of the ACM (JACM)
A Randomized Algorithm for Principal Component Analysis
SIAM Journal on Matrix Analysis and Applications
An experimental evaluation of a Monte-Carlo algorithm for singular value decomposition
PCI'01 Proceedings of the 8th Panhellenic conference on Informatics
Stochastic algorithms in linear algebra: beyond the Markov chains and von Neumann-Ulam scheme
NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
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Abstract: Sparsified Randomization Monte Carlo (SRMC) algorithms introduced in our recent paper [60] for solving systems of linear algebraic equations are extended to construct the SVD-based randomized low rank approximations for large matrices. We suggest some efficient implementations of SRMC based on low rank approximations, and give different applications. In particular, an important application we present in this paper is a fast simulation algorithm for a randomized approximation of non-homogeneous random fields based on a discrete version of the Karhunen-Loeve expansion. We present two examples of non-homogeneous random field simulation which include a long-correlated Lorenzian random field and the fractional Wiener process. Another application we deal in this paper concerns the randomized solvers for large linear systems. We suggest a hybrid method which combines SRMC with an algorithm for solving boundary integral equations based on a separation representation of the kernel. This method is illustrated in this paper by solving a 2D boundary integral equation from potential theory governing the Dirichlet problem for the Laplace equation.