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These systems are built from subsystems that radiate out from an irreducible subsystem that can be stabilized using some other method. Because of this recursive structure, the designer can start the design process at the known-stable system and "back out" new controllers that progressively stabilize each outer subsystem. The process terminates ...
The backward Euler method is an implicit method: the new approximation + appears on both sides of the equation, and thus the method needs to solve an algebraic equation for the unknown +. For non-stiff problems, this can be done with fixed-point iteration:
This is called "zero-stability" because it is enough to check the condition for the differential equation ′ = (Süli & Mayers 2003, p. 332). If the roots of the characteristic polynomial ρ all have modulus less than or equal to 1 and the roots of modulus 1 are of multiplicity 1, we say that the root condition is satisfied.
Instead of repeating step two to convergence, it may be formulated and solved as a set of linear equations. These equations are merely obtained by making = ′ in the step two equation. [clarification needed] Thus, repeating step two to convergence can be interpreted as solving the linear equations by relaxation.
Bellman showed that a dynamic optimization problem in discrete time can be stated in a recursive, step-by-step form known as backward induction by writing down the relationship between the value function in one period and the value function in the next period. The relationship between these two value functions is called the "Bellman equation".
The backward differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations.They are linear multistep methods that, for a given function and time, approximate the derivative of that function using information from already computed time points, thereby increasing the accuracy of the approximation.
Backing out of the deal if it’s just a verbal offer, or before a contract has been signed, is relatively simple. However, once a legal purchase contract has been signed, it becomes much more ...
The short BB step size is same as a linearized minimum-residual step. BB applies the step sizes upon the forward direction vector for the next iterate, instead of the prior direction vector as if for another line-search step. Barzilai and Borwein proved their method converges R-superlinearly for quadratic minimization in two dimensions.