Symmetric Positive-Definite Constitutive Matrices for Discrete Eddy-Current Problems

Symmetric Positive Definite Based Preconditioners For Discrete Convection-diffusion Problems

We experimentally examine the performance of preconditioners based on entries of the symmetric positive definite part and small subspace solvers for linear system of equations obtained from the high-order compact discretization of convection-diffusion equations. Numerical results are described to illustrate that the preconditioned GMRES algorithm converges in a reasonable number of iterations.

DDtBe for Band Symmetric Positive Definite Matrices

We present a new parallel factorization for band symmetric positive definite (s.p.d) matrices and show some of its applications. Let A be a band s.p.d matrix of order n and half bandwidth m. We show how to factor A as A =DDt Be using approximately 4nm2 jp parallel operations where p =21: is the number of processors. Having this factorization, we improve the time to solve Ax = b by a factor of m...

Symmetric Coupling for Eddy Current Problems

Supervised LogEuclidean Metric Learning for Symmetric Positive Definite Matrices

Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for symmetric positive definite (SPD) matrices such as covariance matrices, which arise in many real-world applications. Naively using standard Mahalanobis metric learning methods under the Euclidean geometry for SPD matric...

"Compress and eliminate" solver for symmetric positive definite sparse matrices

We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in. The systems that have efficient compression of the fill-in mostly arise from discretization of partial differential equations. We show that the resulting fa...