نتایج جستجو برای: newton iteration method
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Newton’s iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton’s method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to...
Newton iteration is known (under some precise conditions) to converge quadratically to zeros of non-degenerate systems of polynomials. This and other properties may be used to obtain theorems on the global complexity of solving systems of polynomial equations (See Shub and Smale in 6]), using a model of computability over the reals. However, it is not practical (and not desirable) to actually c...
Newton iteration is known (under some precise conditions) to converge quadratically to zeros of non-degenerate systems of polynomials. This and other properties may be used to obtain theorems on the global complexity of solving systems of polynomial equations (See Shub and Smale in [6]), using a model of computability over the reals. However, it is not practical (and not desirable) to actually ...
Image reconstruction gives rise to some challenging large-scale constrained optimization problems. We consider a convex minimization problem with nonnegativity constraints that arises in astronomical imaging. To solve this problem, we use an efficient hybrid gradient projection-reduced Newton (active-set) method. By "reduced Newton," we mean that we take Newton steps only in the inactive variab...
This paper will concentrate on contributions of CWI to the development of parallel Runge-Kutta (RK) methods. We shall describe two approaches to construct such methods. In both approaches, a conventional implicit RK method is used as a corrector equation whose solution is approximated by an iterative method. In the first approach, the iteration method uses a fixed number of iterations without s...
This paper presents an overlapped block-parallel Newton method for solving large nonlinear systems. The graph partitioning algorithms are first used to partition the Jacobian into weakly coupled overlapping blocks. Then the simplified Newton iteration is directly performed, with the diagonal blocks and the overlapping solutions assembled in a weighted average way at each iteration. In the algor...
Preconditioners for the Conjugate Gradient method are studied to solve the Newton system with symmetric positive definite (SPD) Jacobian. Following the theoretical work in [1] we start from a given approximation of the inverse of the initial Jacobian, and we construct a sequence of preconditioners by means of a low rank update, for the linearized systems arising in the Picard-Newton solution of...
We introduce the concept of a Markov risk measure and we use it to formulate risk-averse control problems for two Markov decision models: a finite horizon model and a discounted infinite horizon model. For both models we derive risk-averse dynamic programming equations and a value iteration method. For the infinite horizon problem we also develop a risk-averse policy iteration method and we pro...
We investigate the solution of the Lyapunov equation with the matrix sign function method. In order to obtain the factorized solution we use a partitioned Newton iteration, where one part of the iteration uses formatted arithmetic for the hierarchical matrix format while the other part converges to an approximate full-rank factor of the solution.
New high order implicit-explicit Runge-Kutta methods have been developed and implemented into a finite volume code to solve the Navier-Stokes equations for reacting gas mixtures. The resulting nonlinear systems in each stage are solved by Newton’s method. If only the chemistry is treated implicitly, the linear systems in each Newton iteration are simple and solved directly. If in addition certa...
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