The paper analyses various parallel incomplete factorizations based on the non-overlapping domain decomposition. The general framework is applied to the investigation of the preconditioning step in cg-like methods. Under certain conditions imposed on the nite element mesh, all matrix and vector types given by the special data distribution can be used in the matrix-by-vector multiplications. Not...

Bayesian statistical inference for an inverse correlation matrix is challenging due to non-linear constraints placed on the matrix elements. The aim of this paper is to present a new parametrization for the inverse correlation matrix, in terms of the Cholesky decomposition, that is able to model these constraints explicitly. As a result, the associated computational schemes for inference based ...

During initialization, discrete multitone receivers train a time domain equalizer (TEQ) to shorten the channel impulse response to a preset length, ν + 1. Arslan, Kiaei, and Evans report a Minimum Intersymbol Interference (Min-ISI) method for TEQ design. Min-ISI TEQs give the highest bit rates among single-FIR TEQs amenable to real-time implementation on programmable fixed-point digital signal ...

In this paper we analyze the efficacy of the LAPACK blocked routine for the Cholesky factorization of symmetric positive definite band matrices on Intel SMP platforms using two multithreaded implementations of BLAS. We also propose strategies that alleviate some of the performance degradation that is observed, and which is basically due to the use of multiple threads when dealing with problems ...

The updating and downdating of QR decompositions has important applications in a number of areas. There is essentially one standard updating algorithm, based on plane rotations, which is backwards stable. Three downdating algorithms have been treated in the literature: the LINPACK algorithm, the method of hyperbolic transformations, and Chambers' algorithm. Although none of these algorithms is ...

The modified Cholesky factorization of Gill and Murray plays an important role in optimization algorithms. Given a symmetric but not necessarily positive definite matrix A, it computes a Cholesky factorization ofA +E, where E= if A is safely positive definite, and E is a diagonal matrix chosen to make A +E positive definite otherwise. The factorization costs only a small multiple of n 2 operati...