Search results for "Positive-definite matrix"
showing 10 items of 22 documents
From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture
2020
Abstract In this paper we study the joint convexity/concavity of the trace functions Ψ p , q , s ( A , B ) = Tr ( B q 2 K ⁎ A p K B q 2 ) s , p , q , s ∈ R , where A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of ( p , q , s ) ∈ R 3 for Ψ p , q , s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of ( α , z ) for α-z Renyi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψ p…
A SYMMETRIC AND POSITIVE DEFINITE BEM FOR 2-D FORCED VIBRATIONS
1997
A BEM formulation for 2D elastodynamics in the time domain has been presented. The formulation gives a resolving system that involves boundary displacements only. The stiffness and mass matrices of the boundary discretized body are frequency independent, symmetric and positive definite
Direct Numerical Methods for Optimal Control Problems
2003
Development of interior point methods for linear and quadratic programming problems occurred during the 1990’s. Because of their simplicity and their convergence properties, interior point methods are attractive solvers for such problems. Moreover, extensions have been made to more general convex programming problems.
Positive definite functions of finitary isometry groups over fields of odd characteristic
2007
Abstract This paper is part of a programme to describe the lattice of all two-sided ideals in complex group algebras of simple locally finite groups. Here we determine the extremal normalized positive definite functions for finitary groups of isometries, defined over fields of odd characteristic.
Size-intensive decomposition of orbital energy denominators
2000
We introduce an alternative to Almlöf and Häser’s Laplace transform decomposition of orbital energy denominators used in obtaining reduced scaling algorithms in perturbation theory based methods. The new decomposition is based on the Cholesky decomposition of positive semidefinite matrices. We show that orbital denominators have a particular short and size-intensive Cholesky decomposition. The main advantage in using the Cholesky decomposition, besides the shorter expansion, is the systematic improvement of the results without the penalties encountered in the Laplace transform decomposition when changing the number of integration points in order to control the convergence. Applications will…
Comparison between the MHFEM formulation and a 2nd spatial order FV formulation of the linear groundwater flow problem
2008
Mixed and Mixed Hybrid Finite Elements (MHFE) methods have been widely used in the last decade for simulation of groundwater flow problem, petroleum reservoir problems, potential flow problems, etc. The main advantage of these methods is that, unlike the classical Galerkin approach, they guarantee local and global mass balance, as well the flux continuity between inter-element sides. The simple shape of the control volume, where the mass conservation is satisfied, makes also easier to couple this technique with a Finite Volume technique in the time splitting approach for the solution of advection-dispersion problems. In the present paper a new second spatial approximation order Finite Volum…
Lower bounds for eigenvalues of a quadratic form relative to a positive quadratic form
1968
Abstract : A method is presented for the calculation of lower bounds to eigenvalues of operators that arise from variational problems for one quadratic form relative to a positive definite quadratic form. Eigenvalue problems of this kind occur, for example, in the theory of buckling of continuous linear elastic systems. The technique used is a modification of one introduced earlier, (1) sections II and IVB, for the determination of lower bounds to eigenvalues of semi-bounded self-adjoint operators. Other methods for the latter problem can be carried over without essential changes. The particular difficulty in the case we consider is that some operators which enter the calculation for the lo…
Diagrammatic Expansion for Positive Spectral Functions in the Steady-State Limit
2019
Recently, a method was presented for constructing self-energies within many-body perturbation theory that are guaranteed to produce a positive spectral function for equilibrium systems, by representing the self-energy as a product of half-diagrams on the forward and backward branches of the Keldysh contour. We derive an alternative half-diagram representation that is based on products of retarded diagrams. Our approach extends the method to systems out of equilibrium. When a steady-state limit exists, we show that our approach yields a positive definite spectral function in the frequency domain.
Vertex corrections for positive-definite spectral functions of simple metals
2016
We present a systematic study of vertex corrections in the homogeneous electron gas at metallic densities. The vertex diagrams are built using a recently proposed positive-definite diagrammatic expansion for the spectral function. The vertex function not only provides corrections to the well known plasmon and particle-hole scatterings, but also gives rise to new physical processes such as generation of two plasmon excitations or the decay of the one-particle state into a two-particles-one-hole state. By an efficient Monte Carlo momentum integration we are able to show that the additional scattering channels are responsible for the bandwidth reduction observed in photoemission experiments on…
$\gamma W$-box Inside-Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum
2019
I consider the $\gamma W$-box correction to superallowed nuclear $\beta$-decays in the framework of dispersion relations. I address a novel effect of a distortion of the emitted electron energy spectrum by nuclear polarizabilities and show that this effect, while neglected in the literature, is sizable. I estimate its size in the approximation of a linear energy dependence, and using two models that are expected to give the lower and the upper bound. The respective correction to the $\beta^+$ spectrum is estimated to be $\Delta_R(E)=(1.6\pm1.6)\times10^{-4}{E}/{\rm MeV}$ assuming a conservative 100\% uncertainty. The effect is positive-definite and can be observed if a high-precision measur…