Concurrent Computing 6.2.3.1 Domain decomposition Domain decomposition is the process of identifying patterns of functionally repetitive, but independent, computation on data. This is the most common type of decomposition in the case of throughput computing, and it relates to the identification of repeti...
The auxiliary subsystems in subdomains are solved by direct or by the Krylov iterative methods. The parallel implementation of algorithms is based on hybrid programming with MPI-processes and multi-thread computing for the upper and the low levels of iterations, respectively. We describe some ...
In Computer Algebra in Scientific Computing, (LNCS 8660), pages 44-58. Springer International Publishing, 2014.R. Bradford, C. Chen, J.H. Davenport, M. England, M. Moreno Maza, and D. Wilson. Truth table invariant cylindrical algebraic decomposition by regular chains. In Computer Algebra in...
In this work, we present a new definition of weighted coreness for vertices in a weighted graph, by taking into account the weights of vertices, which makes the coreness in unweighted graph be a special case. We propose efficient algorithms for both weighted core decomposition and weighted ...
The most logical is the territorial border of the exporting country, because it is the one used in traditional concepts of value added such as GDP [3]. When defining that perimeter, we should consider that the global Leontief inverse matrix B incorporates, by definition, the value added ...
Of course, when computing a query, we don't know which case is optimal, so we have to try both of them and all possible uu. Just like updates, this can also take O(nlogn)O(nlogn) in the worse case. You may note that we don't have to recompute dist(u,v)dist(u,v) eac...
head direction and running direction. The two objectives were combined by considering the sum of squared differences of the two sets of angles. This definition of running direction was used only to rotate the head direction, and was not used in subsequent analyses. Hyperparameters were chosen such...
Compression Definition Matrix PCA 1. Introduction An important concept in linear algebra is the Single Value Decomposition (SVD). With this technique, we can decompose a matrix into three other matrices that are easy to manipulate and have special properties. In this tutorial, we’ll explain how...
This shift invariance arises because in computing the spectrum, the phase of the Fourier transform is discarded and it is this phase which conveys information about the temporal location of signal components. The spectrum is sufficient to represent the signal's energy distribution over frequency, in...
13.5). As directly computing the inverse of a large matrix is difficult, there is an alternate technique using a transform to make this problem easier and require less computations. Sign in to download full-size image Figure 13.5. Problem to solve: find x. The Cholesky decomposition maps ...