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The locus of points that give the same value in the algorithm, for different values of alpha and beta. The alpha max plus beta min algorithm [1] is a high-speed approximation of the square root of the sum of two squares.
For example, alpha = 31/32 and beta = 13/32 outperforms all of the other examples, and (similarly to most of the others) only requires 2 multiplies and one shift to apply those constants, with similar bit-depth requirements. It might also be worth showing how well 16-bit approximations do (i.e. alpha = 62941/65536 and beta = 26070/65536).
Alpha max or variation, may refer to: Critical angle of attack (α max), the highest nose-up attitude at speed before stalling; An element in the mathematical ...
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In mathematics, a smooth maximum of an indexed family x 1, ..., x n of numbers is a smooth approximation to the maximum function (, …,), meaning a parametric family of functions (, …,) such that for every α, the function is smooth, and the family converges to the maximum function as .
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This pseudocode shows the fail-soft variation of alpha–beta pruning. Fail-soft never returns α or β directly as a node value. Thus, a node value may be outside the initial α and β range bounds set with a negamax function call. In contrast, fail-hard alpha–beta pruning always limits a node value in the range of α and β.
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree.It is an adversarial search algorithm used commonly for machine playing of two-player combinatorial games (Tic-tac-toe, Chess, Connect 4, etc.).