The basic theorem presented shows that the product of a linearly ordered space and a countable (regular) space is normal. We prove that the countable space can be replaced by any of a rather large class of countably tight spaces. Examples are given to prove that monotone normality cannot replace linearly ordered in the base theorem. However, it is shown that the product of a monotonically norma...

lsmr (least squares minimal residual) is an iterative method for the solution of the linear system of equations and leastsquares problems. this paper presents a block version of the lsmr algorithm for solving linear systems with multiple right-hand sides. the new algorithm is based on the block bidiagonalization and derived by minimizing the frobenius norm of the resid ual matrix of normal equa...

We explore the idea of overrelaxation for accelerating the expectation-maximization (EM) algorithm, focusing on preserving its simplicity and monotonic convergence properties. It is shown that in many cases a trivial modification in the M-step results in an algorithm that maintains monotonic increase in the log-likelihood, but can have an appreciably faster convergence rate, especially when EM ...

Consider a rooted tree structure the nodes of which have been labelled monotonically by elements of { 1, 2, . . .,k}, which means that any sequence connecting the root of the tree with a leaf is weakly monotone . For fixed k asymptotic equivalents of the form CA gA °n; 2 (n --oo) to the numbers of such tree structures with n nodes are obtained for the family of extended unary-binary trees (i .e...

A real number x is called k-monotonically computable (k-mc), for constant k > 0, if there is a computable sequence (xn)n∈N of rational numbers which converges to x such that the convergence is k-monotonic in the sense that k · |x−xn| ≥ |x−xm| for any m > n and x is monotonically computable (mc) if it is k-mc for some k > 0. x is weakly computable if there is a computable sequence (xs)s∈N of rat...

In this paper we examine the role of the β-space property (equivalently of the MCM-property) in generalized ordered (GO-)spaces and, more generally, in monotonically normal spaces. We show that a GO-space is metrizable iff it is a β-space with a Gδ-diagonal and iff it is a quasidevelopable β-space. That last assertion is a corollary of a general theorem that any β-space with a σ-point-finite ba...