The Kernel polynomial method ~KPM! has been successfully applied to tight-binding electronic-structure calculations as an O(N) method. Here we extend this method to nonorthogonal basis sets with a sparse overlap matrix S and a sparse Hamiltonian H. Since the KPM method utilizes matrix vector multiplications it is necessary to apply SH onto a vector. The multiplication of S is performed using a ...

A new approach is presented for inverse modeling to reconstruct continuous features in space, such as channels, that exhibit sparseness in a complementary basis (e.g. a Fourier basis) using observations in spatial domain. Continuity in space is used to constrain the solution to be sparse in the discrete cosine transform (DCT) domain. The DCT is used to effectively reduce the dimension of the se...

We study a relative optimization framework for quasi-maximum likelihood blind source separation and relative Newton method as its particular instance. The structure of the Hessian allows its fast approximate inversion. In the second part we present Smoothing Method of Multipliers (SMOM) for minimization of sum of pairwise maxima of smooth functions, in particular sum of absolute value terms. In...

Abstract. We extend a structured selected inversion method to the extraction of any arbitrary entry of the inverse of a large sparse matrix A. For various discretized PDEs such as Helmholtz equations, a structured factorization yields a sequence of data-sparse factors of about O(n) nonzero entries, where n is the matrix size. We are then able to extract any arbitrary entry of A 1 in about O(log...

We study a relative optimization framework for quasi-maximum likelihood blind source separation and relative Newton method as its particular instance. The structure of the Hessian allows its fast approximate inversion. In the second part we present Smoothing Method of Multipliers (SMOM) for minimization of sum of pairwise maxima of smooth functions, in particular sum of absolute value terms. In...

This paper describes an application of hierarchical or empirical Bayes to the distributed source reconstruction problem in electro- and magnetoencephalography (EEG and MEG). The key contribution is the automatic selection of multiple cortical sources with compact spatial support that are specified in terms of empirical priors. This obviates the need to use priors with a specific form (e.g., smo...

A parallel computational scheme for analyzing large-scale molecular vibration on distributed memory computing platforms is presented in this paper. This method combines the implicitly restarted Lanczos algorithm with a state-of-art parallel sparse direct solver to compute a set of low frequency vibrational modes for molecular systems containing tens of thousands of atoms. Although the original ...

Non-uniqueness, low computational efficiency and large memory requirements are main issues for geophysical data inversion. In this paper, we propose an efficient algorithm 3D correlationanalysis joint inversion of gravity magnetic with high accuracy computation effort. Firstly, since the number observed field is smaller than inverted parameters, calculations correlation-analysis in model space ...

INTRODUCTION Susceptibility-weighted imaging (SWI) technique is used for neuroimaging to improve visibility of iron deposits, veins, and hemorrhage [1]. Quantitative susceptibility imaging (QSI) improves upon SWI by measuring iron in tissues, which can be useful for molecular/cellular imaging to analyze brain function, diagnose neurological diseases, and quantify contrast agent concentrations. ...

Consider the solution of large sparse symmetric positive de nite linear systems using the preconditioned conjugate gradient method. On sequential architectures, incomplete Cholesky factorizations provide effective preconditioning for systems from a variety of application domains, some of which may have widely di ering preconditioning requirements. However, incomplete factorization based precond...