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In the paper the author presents a novel point of view for the refinement and derefinement algorithms of triangular nested meshes using fractal concepts and iterated function systems (IFS). The fractal behaviour can be understood in the sense that these meshes feature a remarkable amplifying invariance under changes of magnification. Here we compare the meshes obtained by the combination of these algorithms with those presented by Bova and Carey (1992). Although both of the meshes are very similar, the current algorithms automatically build and manage sequences of nested irregular discretizations of the domain. The author illustrates here how the application of IFS families is equivalent to the use of an adaptive strategy that combines the refinement procedure with the derefinement one. [ABSTRACT FROM AUTHOR]

The expectation-maximization (EM) algorithm is a popular approach for obtaining maximum likelihood estimates in incomplete data problems because of its simplicity and stability (e.g. monotonic increase of likelihood). However, in many applications the stability of EM is attained at the expense of slow, linear convergence. We have developed a new class of iterative schemes, called squared iterative methods (SQUAREM), to accelerate EM, without compromising on simplicity and stability. SQUAREM generally achieves superlinear convergence in problems with a large fraction of missing information. Globally convergent schemes are easily obtained by viewing SQUAREM as a continuation of EM. SQUAREM is especially attractive in high-dimensional problems, and in problems where model-specific analytic insights are not available. SQUAREM can be readily implemented as an ‘off-the-shelf’ accelerator of any EM-type algorithm, as it only requires the EM parameter updating. We present four examples to demonstrate the effectiveness of SQUAREM. A general-purpose implementation (written in R) is available. [ABSTRACT FROM AUTHOR]