We analyze the performance-power-energy balance of a conventional Intel Xeon multicore processor and two low-power architectures –an Intel Atom processor and a system with a quad-core ARM Cortex A9+NVIDIA Quadro 1000M– using a high performance implementation of Gauss-Jordan elimination (GJE) for matrix inversion. The blocked version of this algorithm employed in the experimental evaluation most...

Wang proposed a gradient-based neural network (GNN) to solve online matrix-inverses. Global asymptotical convergence was shown for such a neural network when applied to inverting nonsingular matrices. As compared to the previously-presented asymptotical convergence, this paper investigates more desirable properties of the gradient-based neural network; e.g., global exponential convergence for n...

We present families of algorithms for operations related to the computation of the inverse of a Symmetric Positive Definite (SPD) matrix: Cholesky factorization, inversion of a triangular matrix, multiplication of a triangular matrix by its transpose, and one-sweep inversion of an SPD matrix. These algorithms are systematically derived and implemented via the Formal Linear Algebra Methodology E...

We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the target matrix by the scaled Lasso and then adjusts the matrix estimator to be symmetric. The penalty level of the scaled Lasso for each column is completely dete...

Matrices have been used in many analytical and simulation models and numerical solutions. Matrix operations have essential role in many scientific and engineering applications. One of the most time-consuming operations among matrix operations is matrix inversion. Many hardware designs and software algorithms have been proposed to reduce the time of computation. They will be more important for t...

1 Numerical Methods of Analysis in Engineering. Edited by L. E. Grinter, Macmillan Company, New York, 1949, chapter 4. s L. Fox, "Some improvements in the use of relaxation methods for the solution of ordinary and partial differential equations," Royal Soc, London, Proc, v. 190A, 1947, p. 31-59. ' L. Fox & J. C. P. Miller, "Table-making for large arguments. The exponential integral," MTAC, v. 4...

We propose a method for reconstruction of the density matrix from measurable time-dependent (probability) distributions of physical quantities. The applicability of the method based on least-squares inversion is – compared with other methods – very universal. It can be used to reconstruct quantum states of various systems, such as harmonic and and anharmonic oscillators including molecular vibr...