Finite precision computations may affect the stability of algorithms and the accuracy of computed solutions. In this paper we first obtain a relation for computing the number of common significant digits between the exact solution and a computed solution of a one-dimensional initial-value problem obtained by using a single-step or multi-step method. In fact, by using the approximate solutions o...

In Group Synchronization, one attempts to find a collection of unknown group elements from noisy measurements of their pairwise differences. Several important problems in vision and data analysis reduce to group synchronization over various compact groups. Spectral Group Synchronization is a commonly used, robust algorithm for solving group synchronization problems, which relies on diagonalizat...

We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method VHPM . We use this method for solving higher dimensional initial boundary value problemswith variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these prob...

An iterative algorithm is constructed to solve the linear matrix equation pair AXB E, CXD F over generalized reflexive matrix X. When the matrix equation pair AXB E, CXD F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the ...

We propose a knowledge-lean method to generate word puzzles from unstructured and unannotated document collections. The presented method is capable of generating three types of puzzles: odd one out, choose the related word, and separate the topics. The difficulty of the puzzles can be adjusted. The algorithm is based on topic models, semantic similarity, and network capacity. Puzzles of two dif...

We study the accuracy of an algorithm which computes the convolution via Radix-2 fast Fourier transforms. Upper bounds are derived for the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication. These results are compared with the corresponding ones ...

Traditional static topic models mainly focus on the statistical correlation between words, but ignore the sentiment tendency and the temporal properties which may have great effects on topic detection results. This paper proposed an LDA-based dynamic sentiment-topic (DST) model, which could not only detect and track topics but could also analyse the shift of general’s sentiment tendency towards...

Existing algorithms for understanding large collections of documents often produce output that is nearly as difficult and time consuming to interpret as reading each of the documents themselves. Topic modeling is a text understanding algorithm that discovers the “topics” or themes within a collection of documents. Tools based on topic modeling become increasingly complex as the number of topics...

A line-smoothing algorithm based on simple arithmetic is presented and its characteristics are analyzed for various implementations. The algorithm is efficient because it can be implemented using only simple integer arithmetic, with no square root or trigonometric calculations. The algorithm is applicable to graph drawing applications that require smooth polylines between graph nodes. Though th...

An efficient iterative algorithm is applied to seek analytical solutions of higher dimensional initial boundary value problems (IBVPS) with variable coefficients. The proposed scheme finds the solution without any discretization, perturbation, transformation or restrictive assumptions and avoids the round off errors. Numerical results clearly reveal the complete reliability and efficiency of th...