Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 16 November 2020Accepted: 31 August 2021Published online: 21 December 2021Keywordsrandomized numerical linear algebra, incomplete Cholesky factorization, sparse matrix, symmetric diagonally dominant graph Laplacian, random samplingAMS Subject Headings65F08, 65F50, 62D05Pu...

In this paper, we improve the disc separation of the Schur complement of strictly diagonally dominant matrices presented in Liu [SIAM. J. Matrix Anal. Appl., 27 (2005): 665-674]. As applications, we present some new bounds for determinants of original matrices and estimations for eigenvalues of Schur complement. By theoretical analysis, we improve the bounds of determinants established in Huang...

We give a matrix factorization for the solution of the linear system Ax = f , when coefficient matrix A is a dense symmetric positive definite matrix. We call this factorization as "WW T factorization". The algorithm for this factorization is given. Existence and backward error analysis of the method are given. The WDWT factorization is also presented. When the coefficient matrix is a symmetric...

If each off-diagonal entry and the sum of each row of a diagonally dominant M -matrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precisio...

The class of nonlinear systems described by a discrete-time state equation containing a diagonal nonlinear term as in recurrent neural networks is considered. Suf-cient conditions are derived for the stability and induced norm of such systems using positive deenite diagonally dominant Lyapunov functions or storage functions , satisfying appropriate Linear Matrix Inequalities. Preliminary result...

In this paper, we consider the system of linear equations Ax̃ = b̃, where A ∈ Rn×n is a crisp H-matrix and b̃ is a fuzzy n-vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The results can also be used for the class of M-matrices and strictly diagonally dominant matrices. Finally, some numerical examples are given to illustrate the presented theoretical r...

We present a family of linear regression estimators that provides a fine-grained tradeoff between statistical accuracy and computational efficiency. The estimators are based on hard thresholding of the sample covariance matrix entries together with `2-regularizion (ridge regression). We analyze the predictive risk of this family of estimators as a function of the threshold and regularization pa...