A minimax approximation algorithm (or L∞ approximation or uniform approximation) is a method to find an approximation of a mathematical function that minimizes maximum error.[1][2]
For example, given a function defined on the interval and a degree bound , a minimax polynomial approximation algorithm will find a polynomial of degree at most to minimize
[3]
^Muller, Jean-Michel; Brisebarre, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Stehlé, Damien; Torres, Serge (2010). Handbook of Floating-Point Arithmetic (1 ed.). Birkhäuser. p. 376. doi:10.1007/978-0-8176-4705-6. ISBN 978-0-8176-4704-9. LCCN 2009939668.
^Phillips, George M. (2003). "Best Approximation". Interpolation and Approximation by Polynomials. CMS Books in Mathematics. Springer. pp. 49–11. doi:10.1007/0-387-21682-0_2. ISBN 0-387-00215-4.
^Powell, M. J. D. (1981). "7: The theory of minimax approximation". Approximation Theory and Methods. Cambridge University Press. ISBN 0521295149.
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trigonometric function is generated ahead of time using some approximation of a minimaxapproximationalgorithm. For very high precision calculations, when series-expansion...
transportation planning. Any algorithm for the widest path problem can be transformed into an algorithm for the minimax path problem, or vice versa, by...
characterization of optimal solutions, and algorithms for their exact computation, and less with learning or approximation, particularly in the absence of a mathematical...
} is either -1 or +1. Several minimaxapproximationalgorithms are available, the most common being the Remez algorithm. Golomb, Michael (1962). Lectures...
state-of-the-art algorithm is due to Avidor, Berkovitch and Zwick, and its approximation ratio is 0.7968. They also give another algorithm whose approximation ratio...
Panos M. (eds.), "Determining the Performance Ratio of Algorithm Multifit for Scheduling", Minimax and Applications, Nonconvex Optimization and Its Applications...
(2005), "ApproximationAlgorithms for the Capacitated Minimum Spanning Tree Problem and Its Variants in Network Design", ACM Trans. Algorithms, 1 (2):...
assignment to the variables in the clauses. We say that an algorithm A provides an α-approximation to MAXEkSAT if, for some fixed positive α less than or...
exhibit well behaved relative error. Other means of polynomial approximation, such as minimax optimization, may be used to control both kinds of error. Many...
than 1.463. The currently best known approximationalgorithm achieves approximation ratio of 1.488. The minimax facility location problem seeks a location...
that have a polynomial time approximationalgorithm that achieves a constant approximation ratio. Although such approximations are not known for the feedback...
difference learning can be used to learn state evaluation constants for a minimax AI playing a simple board game. Reinforcement Learning Problem, document...
{\hat {\lambda }}_{i}=X_{i}} is inadmissible. In this case, a family of minimax estimators is given for any 0 < c ≤ 2 ( p − 1 ) {\displaystyle 0<c\leq...
first used by Bernstein in a constructive proof for the Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials...
greater complexity for non-perfect graphs. In addition, several important minimax theorems in combinatorics, including Dilworth's theorem and Mirsky's theorem...
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