Information om | Engelska ordet FIXED-POINT

Exempel på hur man kan använda FIXED-POINT i en mening

• Among hundreds of fixed-point theorems, Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics.
• Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x, f (x), f (f (x)), f (f (f (x))),.
• It supports recursion, structured programming, linked data structure handling, fixed-point, floating-point, complex, character string handling, and bit string handling.
• A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixed-point theorem.
• All but the only partially compatible Model 44 and the most expensive systems use microcode to implement the instruction set, featuring 8-bit byte addressing and fixed-point binary, fixed-point decimal and hexadecimal floating-point calculations.
• The functionality of the library includes support for basic 2D graphics, image manipulation, text output, audio output, MIDI music, input and timers, as well as additional routines for fixed-point and floating-point matrix arithmetic, Unicode strings, file system access, file manipulation, data files, and 3D graphics.
• In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces and provides a constructive method to find those fixed points.
• A floating-point data type is a compromise between the flexibility of a general rational number data type and the speed of fixed-point arithmetic.
• Along with the basic central processing unit (CPU) the system could also have had a floating-point unit (the "Auxiliary Arithmetic Unit"), or a fixed-point decimal option with three six-bit decimal digits per word.
• Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating-point representation with a fixed number of significant digits.
• The proof most commonly seen in textbooks relies on the contraction mapping principle, also known as the Banach fixed-point theorem (which can also be used as the key step in the proof of existence and uniqueness of solutions to ordinary differential equations).
• Using again just the syntactic transformations available in this formalism, one can obtain so-called fixed-point combinators (the best-known of which is the Y combinator); these, by definition, have the property that f(Y(f)) = Y(f) for all functions f.
• A contraction mapping may then be thought of as a way of approximating the final result of a computation (which can be guaranteed to exist by the Banach fixed-point theorem).
• Abelson graduated with a Bachelor of Arts degree in mathematics from Princeton University in 1969 after completing a senior thesis on Actions with fixed-point set: a homology sphere, supervised by William Browder.
• Since most modern processors have fast floating-point unit (FPU), fixed-point representations in processor-based implementations are now used only in special situations, such as in low-cost embedded microprocessors and microcontrollers; in applications that demand high speed or low power consumption or small chip area, like image, video, and digital signal processing; or when their use is more natural for the problem.
• Replacement: Kolmogorov proved that the five properties of symmetry, fixed-point, monotonicity, continuity, and replacement fully characterize the quasi-arithmetic means.
• In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem.
• Schauder is best known for the Schauder fixed-point theorem, which is a major tool to prove the existence of solutions in various problems, the Schauder bases (a generalization of an orthonormal basis from Hilbert spaces to Banach spaces), and the Leray−Schauder principle, a way to establish solutions of partial differential equations from a priori estimates.
• This work anticipates a number of later theories, such as the general theory of algebraic correspondences, Hecke operators, and Lefschetz fixed-point theorem.
• There are a number of generalisations to Banach fixed-point theorem and further; these are applied in PDE theory.

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