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- W2151603610 abstract "In this paper, we study the general question of how characteristics of functional equations influence whether or not they are robust. We isolate examples of properties which are necessary for the functional equations to be robust. On the other hand, we show other properties which are sufficient for robustness. We then study a general class of functional equations, which are of the form $forall x,y F[f(x-y), f(x+y), f(x),f(y)]=0, where F is an algebraic function. We give conditions on such functional equations that imply robustness. Our results have applications to the area of self-testing/correcting programs. We show that self-testers and self-correctors can be found for many functions satisfying robust functional equations, including algebraic functions of trigonometric functions such as $tan{x},{1 over {1+cot{x}}},$ ${Ax over {1-Ax}},cosh x." @default.
- W2151603610 created "2016-06-24" @default.
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- W2151603610 date "1999-01-01" @default.
- W2151603610 modified "2023-09-24" @default.
- W2151603610 title "On the Robustness of Functional Equations" @default.
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- W2151603610 doi "https://doi.org/10.1137/s0097539796298625" @default.
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