منابع مشابه
Several Parallel Algorithms for Solving Nonlinear Systems with Symmetric and Positive Definite Jacobians
In this work we describe two sequential algorithms and their parallel counterparts for solving nonlinear systems, when the Jacobian matrix is symmetric and positive definite. This case appears frequently in unconstrained optimization problems. Both algorithms are based on Newton’s method. The first solves the inner iteration with Cholesky decomposition while the second is based on the inexact N...
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In this contribution, we focus on a class of nonlinear positive systems, arising especially in biological processes. These are SISO input-affine systems with a nonlinear measurable drift. We develop a positive output feedback control law for these systems and prove the global asymptotic stability of an equilibrium point for the closed loop systems, that can be set on a model-dependent surface. ...
متن کاملParallel Numerical Algorithms for Symmetric Positive Definite Linear Systems
We give a matrix factorization for the solution of the linear system Ax = f , when coefficient matrix A is a dense symmetric positive definite matrix. We call this factorization as "WW T factorization". The algorithm for this factorization is given. Existence and backward error analysis of the method are given. The WDWT factorization is also presented. When the coefficient matrix is a symmetric...
متن کاملPT -symmetric nonlinear metamaterials and zero-dimensional systems
A one dimensional, parity-time (PT )-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken PT -phase is determined through the calculation of the eigenfrequency spectrum for two different configurations; the one with equidistant split-rings and the other with the split-rings f...
متن کاملNonlinear modes in finite-dimensional PT-symmetric systems.
By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear properties of the systems undergo significant changes. On an example of an array of four waveguides described by the discrete nonlinear Schrödinger equation with...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 1992
ISSN: 0294-1449
DOI: 10.1016/s0294-1449(16)30231-1