We study the convex body e L n deened by e L n := fX j X = (x ij) positive semideenite n n matrix ; x ii = 1 for all ig: Our main motivation for investigating this body comes from combinatorial optimization, namely from approximating the max-cut problem. An important property of e L n is that, due to the positive semideenite constraints, one can optimize over it in polynomial time. On the other...

A numerical method for computing the logarithm of a symmetric positive dee-nite matrix is developed in this paper. It is based on reducing the original matrix to a tridiagonal matrix by orthogonal similarity transformations and applying Pad e approximations to the logarithm of the tridiagonal matrix. Theoretical studies and numerical experiments indicate that the method is quite eecient when th...

Based on a particular node ordering and corresponding block decomposition of the matrix we analyse an e cient, algebraic multilevel preconditioner for the iterative solution of nite element discretizations of elliptic boundary value problems. Thereby an analysis of a new version of block-factorization preconditioning methods is presented. The approximate factorization requires an approximation ...

This paper presents a su cient condition on sparsity patterns for the existence of the incomplete Cholesky factorization. Given the sparsity pattern P (A) of a matrix A, and a target sparsity pattern P satisfying the condition, incomplete Cholesky factorization successfully completes for all symmetric positive de nite matrices with the same pattern P (A). It is also shown that this condition is...

In this paper we propose a new multivariate GARCH model with timevarying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. While each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analogue. By impos...

We demonstrate that if A1; :::; Am are symmetric positive semide nite n n matrices with positive de nite sum and A is an arbitrary symmetric n n matrix, then the quality of the semide nite relaxation max X fTr(AX) j Tr(AiX) 1; i = 1; :::;m; X 0g (SDP) of the optimization program xTAx! max j xTAix 1; i = 1; :::;m (P) is not worse than 1 2 ln(2m2) . It is shown that this bound is sharp in order, ...

We demonstrate that if A1; :::; Am are symmetric positive semide nite n n matrices with positive de nite sum and A is an arbitrary symmetric n n matrix, then the quality of the semide nite relaxation max X fTr(AX) j Tr(AiX) 1; i = 1; :::;m; X 0g (SDP) of the optimization program xTAx! max j xTAix 1; i = 1; :::;m (P) is not worse than 1 2 ln(2m2) . It is shown that this bound is sharp in order, ...

This work delves into the liquidations mechanism inherent in Decentralised Finance (DeFi) lending protocols and connection between price volatility decentralised exchanges (DEXs). The analysis employs transactional data of three largest DeFi provides evidence a positive relation post-liquidations across main DEX pools. Without directly observing behaviour liquidators, these findings indirectly ...

Given a nonsingular matrix A, and a nonnegative matrix T , under certain very mild conditions, there is a unique splitting A = B C, such that T = B 1 C. Moreover, all properties of the splitting are derived directly from the iteration matrix T . These results do not hold when the matrix A is singular. It is shown that given a nonnegative matrix T and a splitting A = B C such that T = B 1 C, the...

Certain matrix relationships play an important role in optimality conditions and algorithms for nonlinear and semideenite programming. Let H be an n n symmetric matrix, A an m n matrix, and Z a basis for the null space of A. (In the context of optimization, H is the Hessian of a smooth function and A is the Jacobian of a set of constraints.) When the reduced Hessian Z T HZ is positive deenite, ...