this study develops and analyzes preconditioned krylov subspace methods to solve linear systemsarising from discretization of the time-independent space-fractional models. first, we apply shifted grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. then, we employee two preconditioned iterative methods, namely, the preconditioned gene...

Interior point methods for semide nite optimization have recently been studied intensively, due to their polynomial complexity and practical e ciency. Many search directions have been proposed to symmetrize the corresponding Newton system. In this paper, we rst introduce a variational principle for de ning the search direction and show that the Nesterov-Todd (NT) direction is optimal under this...

Approximate nearest neighbor (ANN) search has achieved great success in many tasks. However, existing popular methods for ANN search, such as hashing and quantization methods, are designed for static databases only. They cannot handle well the database with data distribution evolving dynamically, due to the high computational effort for retraining the model based on the new database. In this pa...

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Finding efficient and physically based methods to interactively simulate deformable objects is a challenging issue. The most promising methods addressing this issue are based on finite elements and multigrid solvers. However, these multigrid methods still suffer, when used to simulate large deformations, from two pitfalls, depending on the kind of grids hierarchy used. If embedded grids are use...

Motivated by grammatical inference and data compression applications, we propose an algorithm to update a suffix array after the substitution, in the indexed text, of some occurrences of a given word by a new character. Compared to other published index update methods, the problem addressed here may require the modification of a large number of distinct positions over the original text. The pro...

Based on a new kernel function, a large-update primal-dual interior-point algorithm for solving linear optimization is proposed. The kernel function is used both for determining the search directions and for measuring the distance between the given iterate and the μ-center for the algorithm. By using several new technical lemmas, the iteration complexity bound as O( √ n log n log nε ) is obtain...

Primal-dual interior-point methods (IPMs) have shown their power in solving large classes of optimization problems. However, at present there is still a gap between the practical behavior of these algorithms and their theoretical worst-case complexity results, with respect to the strategies of updating the duality gap parameter in the algorithm. The so-called small-update IPMs enjoy the best kn...

A family of secant methods based on general rank-1 updates has been revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broy-den's "good" and "bad" update techniques play a special role — but should be associated with two different line search principles. For Broyden's "bad" update technique, a minimum residual principle is na...

Given a large network, computing statistics such as clustering coefficient, or modularity, is costly for large networks. When one more edge or vertex is added, traditional methods require that the full (expensive) computation be redone on this slightly modified graph. Alternatively, we introduce here a new approach: under modification to the graph, we update the statistics instead of computing ...