fixed point

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fixed point

[¦fikst ′pȯint]
(engineering)
A reproducible value, as for temperature, used to standardize measurements; derived from intrinsic properties of pure substances.
(mathematics)
For a function ƒ mapping a set S to itself, any element of S which ƒ sends to itself.

Fixed Point

 

a form of representation of numbers in a digital computer with constant position of the point that sepa-rates the whole part of the number from the fraction. The fixed point corresponds to the natural form of representation of numbers. The point may be fixed at any position of the number—for example, in a digital computer five-place numbers with a fixed point after the second place are represented as +74.531, +07.453, +00.745, and so on. To prevent the numbers formed in the process of calculations from going beyond the range of representable numbers, scale factors are incorporated into the input data and intermediate and final results when drawing up programs for computers with a fixed point. However, the fixing of the point before the high-order digit of the modulus of the number (a number less than 1) is more expedient; in such a case the word format of the digital computer is not overloaded during multiplication of numbers. The range of representable numbers is narrower in a digital computer with a fixed point than in a digital computer with a floating point. The complication of programming when a fixed point is used is compensated in some cases by the simplicity of the devices of the digital computer and the ease in carrying out arithmetic operations, and also by the possibility of achieving greater speed in addition and subtraction. A fixed point was used in the Soviet Minsk-1, Setun’, and Ural-1 digital computers and in most digital control computers.

A. V. GUSEV

fixed point

(mathematics)
The fixed point of a function, f is any value, x for which f x = x. A function may have any number of fixed points from none (e.g. f x = x+1) to infinitely many (e.g. f x = x). The fixed point combinator, written as either "fix" or "Y" will return the fixed point of a function.

See also least fixed point.

fixed point

A method for storing and calculating numbers in which the decimal point is always in the same location. Contrast with floating point.
References in periodicals archive ?
Kamran, "Coincidence and fixed points for hybrid strict contractions," Journal of Mathematical Analysis and Applications, vol.
Thus, by linearity of expectation, the expected number of fixed points in a random permutation is exactly 1, no matter the size.
Xu: Iterative methods for finding minimum-norm fixed points of nonexpansive mappings with applications, Optimization, 60(2011), No.
In any case, if conscious moments correspond only to fixed points, this puts serious constraints on the nature of the fixed points, as we shall discuss.
Jungck, fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J.
Now, we consider the following iteration introduced by Schu [9] for approximation of fixed points of Lipschitz pseudocontractive maps.
We are interested in the task of computing fixed points and N-cycles for the well known and much studied discrete logistic equation
Besides 6560 mobile health teams, he informed that anti-polio drops were also administered to children of the required age at 766 fixed points, 277 transit points and 73 border points with objective to ensure hundred percent coverage during the campaign.
1 : any of the heavenly bodies except planets which are visible at night and look like fixed points of light
basic measurements (control of the track identification network, survey of lanes and switches, fixed points for the free space profile, etc.
Turning to set-valued analysis, they consider such topics as the Hausdorff metric and the distance between sets, upper and lower semi-continuous set-valued maps, fixed points and coincidences of maps in metric spaces, and topological degree and fixed points of set-valued maps in Banach spaces.
The notion of normal structure was introduced by Brodskii and Milman (see [4]), when they studied fixed points of isometries.