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Backward induction is the process of reasoning backwards in time from the end of a problem or situation to determine a sequence of optimal actions. It proceeds by examining the last point at which a decision is to be made and then identifying what action would be most optimal at that moment.

The forward– backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions ::= … i.e. it computes for all hidden state variables ∈ { … } the distribution ( | :).This inference task is usually called smoothing.The algorithm makes use of the principle of dynamic …

Worked-example effect – Wikipedia

Backward Euler method – Wikipedia

Dynamic programming – Wikipedia

Forward–backward algorithm – Wikipedia

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 :

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 a…