In this paper, we present a block version of incomplete LU preconditioner which is computed as the by-product of block A-biconjugation process. The pivot entries of this block preconditioner are one by one or two by two blocks. The L and U factors of this block preconditioner are computed separately. The block pivot selection of this preconditioner is inherited from one of the block versions of...

We prove that standard Gaussian random multipliers are expected to stabilize numerically both Gaussian elimination with no pivoting and block Gaussian elimination. Our tests show similar results where we applied circulant random multipliers instead of Gaussian ones.

Consider the linear system of equations of the form Ax = b where the coefficient matrix A ∈ Rn×n is nonsingular, large, sparse and nonsymmetric and also x, b ∈ R. We refer to this system as the original system. An explicit preconditioner M for this system is an approximation of matrix A−1. In [1], Lou presented the Backward Factored INVerse or BFINV algorithm which computes the inverse factoriz...

We propose a method of solving large sparse systems of homogeneous linear equations over GF(2), the field with two elements. We modify an algorithm due to Wiedemann. A block version of the algorithm allows us to perform 32 matrix-vector operations for the cost of one. The resulting algorithm is competitive with structured Gaussian elimination in terms of time and has much lower space requiremen...

In this paper two new fading distributions, the α−η−μ Distribution and α−κ−μ Distribution, are presented. The α − η − μ distribution includes the α − μ, Nakagami-m, Nakagami-q, Weibull, Hoyt, Rayleigh, Exponential, and the OneSided Gaussian distributions as special cases. The α − κ − μ distribution includes the α − μ, Nakagami-m, Weibull, Rice, Rayleigh, Exponential, and the One-Sided Gaussian ...

We consider the sequential Bayesian op-timization problem with bandit feedback,adopting a formulation that allows for the re-ward function to vary with time. We modelthe reward function using a Gaussian pro-cess whose evolution obeys a simple Markovmodel. We introduce two natural extensionsof the classical Gaussian process upper confi-dence bound (GP-UCB) algorit...

A generalization of Finsler structures on surfaces is proposed and the differential invariants of such structures are developed. The information obtained is then used to construct examples of Finsler structures and generalized Finsler structures which satisfy various interesting curvature conditions. In particular, examples are constructed of non-Riemannian Finsler structures on the 2-sphere wh...