Now showing items 1-10 of 27
A Variable-Metric Variant of the Karmarkar Algorithm for Linear Programming
The most time-consuming part of the Karmarkar algorithm for linear programming is computation of the step direction, which requires the projection of a vector onto the nullspace of a matrix that changes at each iteration. ...
Inference for Time Series with Mixed Spectrum
The old and important problem of estimating the discontinuous (mixed) spectrum of a series containing periodic components was considered in this paper. Most nonparametric spectral estimation procedures were developed for ...
Safeguarding Hessian Approximations in Trust Region Algorithms
In establishing global convergence results for trust region algorithms applied to unconstrained optimization, it is customary to assume either a uniform upper bound on the sequence of Hessian approximations or an upper ...
Karmarkar as a Classical Method
In this work we demonstrate that the Karmarkar algorithm for linear programs results from the classical approach of first transforming nonnegativity constraints into equality constraints by adding squared-slack variables ...
Domain Decomposition and Mixed Finite Element Methods for Elliptic Problems
In this paper we describe the numerical solution of elliptic problems with nonconstant coefficients by domain decomposition methods based on a mixed formulation and mixed finite element approximations. Two families of ...
Projected Newton for the Symmetric Eigenvalue Problem has Order 1+sqrt(2)
In their study of the classical inverse iteration algorithm, Peters and Wilkinson considered the closely related algorithm that consists of applying Newton's method, followed by a 2-norm normalization, to the nonlinear ...
Domain Decomposition for Elliptic Partial Differential Equations with Neumann Boundary Conditions
Discretization of a self-adjoint elliptic partial differential equation by finite differences or finite elements yields a large, sparse, symmetric system of equations, Ax=b. We use the preconditioned conjugate gradient method with domain decomposition to develop an effective, vectorizable preconditioner which is suitable for solving large two-dimensional problems on vector and parallel machines....
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