We describe PP-BCG, a parallel iterative solver for the solution of dense and symmetric positive-definite linear systems with multiple right-hand sides suitable for MPPs. Such linear systems appear in the context of stochastic estimation of the diagonal of the matrix inverse in Uncertainty Quantification and the trace of matrix products in statistical analysis. We propose a novel numerical sche...

This paper deals with the linear system x′ = A(t)x with A(t) being a 2× 2 matrix. The anti-diagonal components of A(t) are assumed to be periodic, but the diagonal components are not necessarily periodic. Our concern is to establish sufficient conditions for the zero solution to be attractive. Floquet theory is of no use in solving our problem, because not all components are periodic. Another a...

Theoretical analysis of randomized, compressive operators often depends on a concentration of measure inequality for the operator in question. Typically, such inequalities quantify the likelihood that a random matrix will preserve the norm of a signal after multiplication. When this likelihood is very high for any signal, the random matrices have a variety of known uses in dimensionality reduct...

In the present work we show that joint probability distribution of eigenvalues can be expressed in terms a differential operator acting on some other matrix quantities. Those quantities might diagonal or pseudo-diagonal entries as it is case for Hermitian matrices. These representations are called derivative principles. We them additive spaces Hermitian, antisymmetric, anti-self-dual, and compl...

We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph defined by the consensus matrix and the eigenvalues of the associated transition probability matrix are used to determine the number of clusters. For noisy or high...

The error backpropagation (EBP) algorithm for training feedforward multilayer perceptron (FMLP) has been used in many applications because it is simple and easy to implement. However, its gradient descent method prevents EBP algorithm from converging fast. To overcome the slow convergence of EBP algorithm, the second order methods have adapted. Levenberg-Marquardt (LM) algorithm is estimated to...

In this paper, a novel algorithm, Cross Low-dimension Pursuit, based on a new structured sparse matrix, Permuted Block Diagonal (PBD) matrix, is proposed in order to recover sparse signals from incomplete linear measurements. The main idea of the proposed method is using the PBD matrix to convert a high-dimension sparse recovery problem into two (or more) groups of highly low-dimension problems...

The practical visual data do not necessarily lie in linear subspaces, so deep convolutional subspace clustering network is proposed to segment the into multiple categories accurately. original contains stacked encoder module, decoder module and self-expression module. We firstly alter i.e., add a new k-block diagonal regularizer weights of It means that $$\ell _1$$ or _2$$ abandoned. directly p...

a Nearly Tridiagonal Matrix Magdy Tawfik Hanna1 ABSTRACT A fully-fledged definition for the fractional discrete Fourier transform of type IV (FDFT-IV) is presented and shown to outperform the simple definition of the FDFT-IV which is proved to be just a linear combination of the signal, its DFT-IV and their flipped versions. This definition heavily depends on the availability of orthonormal eig...

The idea of preconditioning is usually associated with solution techniques for solving linear systems or eigenvalue problems. It refers to a general method by which the original system is transformed into one which admits the same solution but which is easier to solve. Following this principle we consider in this paper techniques for preconditioning the matrix exponential operator, e A y 0 , us...