DIRECTION-PRESERVING AND SCHUR-MONOTONIC SEMISEPARABLE APPROXIMATIONS OF SYMMETRIC POSITIVE DEFINITE MATRICES∗ MING GU† , XIAOYE S. LI‡ , AND PANAYOT S. VASSILEVSKI§ Abstract. For a given symmetric positive definite matrix A ∈ RN×N , we develop a fast and backward stable algorithm to approximate A by a symmetric positive definite semiseparable matrix, accurate to a constant multiple of any pres...

We establish some general theorems for the existence and nonexistence of ground state solutions of steady-state N coupled nonlinear Schrödinger equations. The sign of coupling constants βij ’s is crucial for the existence of ground state solutions. When all βij ’s are positive and the matrix is positively definite, there exists a ground state solution which is radially symmetric. However, if al...

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

in this paper for a given prescribed ritz values that satisfy in the some special conditions, we nd a symmetric nonnegative matrix, such that the given set be its ritz values.

We investigate spacing statistics for ensembles of various real random matrices where the matrixelements have various Probability Distribution Function (PDF: f(x)) including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derived that spacing distribution p(s) of adjacent energy eigenvalues are distinct. Nevertheless, they show the linear level repulsion near s = 0 as αs...

We revisit the classical H∞ analysis problem of computing the `-induced norm of a linear time-invariant system. We follow an approach based on converting the problem of maximization over signals to that of maximization over a sort of deterministic covariance matrices. The reformulation in terms of these covariance matrices greatly simplifies the dynamic analysis problem and converts the computa...

Over any field F every square matrix A can be factored into the product of two symmetric matrices as A = S1 ·S2 with Si = S i ∈ F and either factor can be chosen nonsingular, as was discovered by Frobenius in 1910. Frobenius’ symmetric matrix factorization has been lying almost dormant for a century. The first successful method for computing matrix symmetrizers, i.e., symmetric matrices S such ...

Abstract: We study the level spacing distribution P (S) of 2D real random matrices both symmetric as well as general, non-symmetric. In the general case we restrict ourselves to Gaussian distributed matrix elements, but different widths of the various matrix elements are admitted. The following results are obtained: An explicit exact formula for P (S) is derived and its behaviour close to S = 0...