Fast Krylov Methods for Clustering

Modification of the Fast Global K-means Using a Fuzzy Relation with Application in Microarray Data Analysis

Recognizing genes with distinctive expression levels can help in prevention, diagnosis and treatment of the diseases at the genomic level. In this paper, fast Global k-means (fast GKM) is developed for clustering the gene expression datasets. Fast GKM is a significant improvement of the k-means clustering method. It is an incremental clustering method which starts with one cluster. Iteratively ...

Fast Preconditioned Krylov Methods for Boundary Integral Equations in Electromagnetic Scattering

New variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs

In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...

Efficient Implementation of Inner-Outer Flexible GMRES for the Method of Moments Based on a Volume-Surface Integral Equation

This paper presents flexible inner-outer Krylov subspace methods, which are implemented using the fast multipole method (FMM) for solving scattering problems with mixed dielectric and conducting object. The flexible Krylov subspace methods refer to a class of methods that accept variable preconditioning. To obtain the maximum efficiency of the inner-outer methods, it is desirable to compute the...

Fast Krylov Methods for N-Body Learning

This paper addresses the issue of numerical computation in machine learning domains based on similarity metrics, such as kernel methods, spectral techniques and Gaussian processes. It presents a general solution strategy based on Krylov subspace iteration and fast N-body learning methods. The experiments show significant gains in computation and storage on datasets arising in image segmentation...