2,835 research outputs found
A Three-Term Conjugate Gradient Method with Sufficient Descent Property for Unconstrained Optimization
Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. Moreover, we present a specific three-term conjugate gradient method based on the multi-step quasi-Newton method. Finally, some numerical results of the proposed method are given
A dynamic model of Venus's gravity field
Unlike Earth, long wavelength gravity anomalies and topography correlate well on Venus. Venus's admittance curve from spherical harmonic degree 2 to 18 is inconsistent with either Airy or Pratt isostasy, but is consistent with dynamic support from mantle convection. A model using whole mantle flow and a high viscosity near surface layer overlying a constant viscosity mantle reproduces this admittance curve. On Earth, the effective viscosity deduced from geoid modeling increases by a factor of 300 from the asthenosphere to the lower mantle. These viscosity estimates may be biased by the neglect of lateral variations in mantle viscosity associated with hot plumes and cold subducted slabs. The different effective viscosity profiles for Earth and Venus may reflect their convective styles, with tectonism and mantle heat transport dominated by hot plumes on Venus and by subducted slabs on Earth. Convection at degree 2 appears much stronger on Earth than on Venus. A degree 2 convective structure may be unstable on Venus, but may have been stabilized on Earth by the insulating effects of the Pangean supercontinental assemblage
An Efficient Hybrid Algorithm for the Separable Convex Quadratic Knapsack Problem
This article considers the problem of minimizing a convex, separable quadratic function subject to a knapsack constraint and a box constraint. An algorithm called NAPHEAP has been developed to solve this problem. The algorithm solves the Karush-Kuhn-Tucker system using a starting guess to the optimal Lagrange multiplier and updating the guess monotonically in the direction of the solution. The starting guess is computed using the variable fixing method or is supplied by the user. A key innovation in our algorithm is the implementation of a heap data structure for storing the break points of the dual function and computing the solution of the dual problem. Also, a new version of the variable fixing algorithm is developed that is convergent even when the objective Hessian is not strictly positive definite. The hybrid algorithm NAPHEAP that uses a Newton-type method (variable fixing method, secant method, or Newton's method) to bracket a root, followed by a heap-based monotone break point search, can be faster than a Newton-type method by itself, as demonstrated in the numerical experiments
Relaxation of Surface Profiles by Evaporation Dynamics
We present simulations of the relaxation towards equilibrium of one
dimensional steps and sinusoidal grooves imprinted on a surface below its
roughening transition. We use a generalization of the hypercube stacking model
of Forrest and Tang, that allows for temperature dependent
next-nearest-neighbor interactions. For the step geometry the results at T=0
agree well with the t^(1/4) prediction of continuum theory for the spreading of
the step. In the case of periodic profiles we modify the mobility for the tips
of the profile and find the approximate solution of the resulting free boundary
problem to be in reasonable agreement with the T=0 simulations.Comment: 6 pages, Revtex, 5 Postscript figures, to appear in PRB 15, October
199
Multiple-rank modifications of a sparse Cholesky factorization.
Given a sparse symmetric positive definite matrix AA T and an associated sparse Cholesky factorization LDL T or LL T , we develop sparse techniques for updating the factorization after either adding a collection of columns to A or deleting a collection of columns from A. Our techniques are based on an analysis and manipulation of the underlying graph structure, using the framework developed in an earlier paper on rank-1 modifications [T. A. Davis and W. W. Hager, SIAM J. Matrix Anal. Appl., 20 (1999), pp. 606-627]. Computationally, the multiple-rank update has better memory traffic and executes much faster than an equivalent series of rank-1 updates since the multiple-rank update makes one pass through L computing the new entries, while a series of rank-1 updates requires multiple passes through L
Profile scaling in decay of nanostructures
The flattening of a crystal cone below its roughening transition is studied
by means of a step flow model. Numerical and analytical analyses show that the
height profile, h(r,t), obeys the scaling scenario dh/dr = F(r t^{-1/4}). The
scaling function is flat at radii r<R(t) \sim t^{1/4}. We find a one parameter
family of solutions for the scaling function, and propose a selection criterion
for the unique solution the system reaches.Comment: 4 pages, RevTex, 3 eps figure
Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators
As a generic model describing quasi-one-dimensional Mott and Peierls
insulators, we investigate the Holstein-Hubbard model for half-filled bands
using numerical techniques. Combining Lanczos diagonalization with Chebyshev
moment expansion we calculate exactly the photoemission and inverse
photoemission spectra and use these to establish the phase diagram of the
model. While polaronic features emerge only at strong electron-phonon
couplings, pronounced phonon signatures, such as multi-quanta band states, can
be found in the Mott insulating regime as well. In order to corroborate the
Mott to Peierls transition scenario, we determine the spin and charge
excitation gaps by a finite-size scaling analysis based on density-matrix
renormalization group calculations.Comment: 5 pages, 5 figure
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