Relations of simulated annealing and quantum annealing are studied by a mapping from the transition matrix of classical Markovian dynamics of the Ising model to a quantum Hamiltonian and vice versa. It is shown that these two operators, the transition matrix and the Hamiltonian, share the eigenvalue spectrum. Thus, if simulated annealing with slow temperature change does not encounter a difficu...

This paper presents a comparative study of two data mapping schemes for parallel sparse LU factorization with partial pivoting on distributed memory machines Our previous work has developed an approach that incorporates static symbolic factoriza tion nonsymmetric L U supernode partitioning and graph scheduling for this problem with D column block mapping The D mapping is commonly considered mor...

Random feature mappings have been successfully used for approximating non-linear kernels to scale up kernel methods. Some work aims at speeding up the feature mappings, but brings increasing variance of the approximation. In this paper, we propose a novel random feature mapping method that uses a signed Circulant Random Matrix (CRM) instead of an unstructured random matrix to project input data...

Computing matrix products is both a central operation in many numerical algorithms and potentially time consuming, making it one of the most well-studied problems in numerical computing. Various algorithms have been devised for computing C = AB, especially for large matrices. Mapping such algorithms to custom or general purpose hardware architecture is always a challenging task. By having a cus...

Kernel based nonlinear feature extraction is feasible to extract the feature of image for classification.The current kernel-based method endures two problems: 1) kernelbased method is to use the data vector through transforming the image matrix into vector, which will cause the store and computing burden; 2) the parameter of kernel function has the heavy influences on kernel based learning meth...

The aim of this article is focused on the design of an obstacle detection system for assisting visually impaired people. A simple Time of Flight camera captures real time images present in the environment of the subject. These images are analyzed using OpenCV and MATLAB for depth and position of objects. The disparity map created is segmented into depth categories. A matrix of this data corresp...

The Perron-Frobenius Theorem says that if A is a nonnegative square matrix some power of which is positive, ihen there exî sts an .v,, such thai A ".\/\\A "x\\ converges to x,j for all .v > 0, There are many classical proofs of this theorem, all depending on a connection between positivily of a matrix and properties of ils eigenvalues. A more modern proof, due to Garrett Birkhoff. is based on t...

This article treats data reduction in array processing for the spatially colored noise case. The purpose is to reduce the computational complexity of the applied signal processing algorithms by mapping the data into a space of lower dimension by means of a linear transformation. We discuss ways to implement the transformation and show that it suffices to estimate the array covariance matrix ins...