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The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
A closed interval is an interval that includes all its endpoints and is denoted with square brackets. [2] For example, [0, 1] means greater than or equal to 0 and less than or equal to 1 . Closed intervals have one of the following forms in which a and b are real numbers such that a ≤ b : {\displaystyle a\leq b\colon }
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
A. Piasecka-Belkhayat, "Interval Boundary Element Method for 2D Transient Diffusion Problem Using the Directed Interval Arithmetic", Engineering Analysis with Boundary Elements, Volume 35, Issue 3, Pages 259–263, 2011.
For any given n ≥ 1, among the polynomials of degree n with leading coefficient 1 (monic polynomials): = is the one of which the maximal absolute value on the interval [−1, 1] is minimal. This maximal absolute value is: 1 2 n − 1 {\displaystyle {\frac {1}{2^{n-1}}}} and | f ( x ) | reaches this maximum exactly n + 1 times at: x = cos ...
Intermediate value theorem: Let be a continuous function defined on [,] and let be a number with () < < ().Then there exists some between and such that () =.. In mathematical analysis, the intermediate value theorem states that if is a continuous function whose domain contains the interval [a, b], then it takes on any given value between () and () at some point within the interval.
In mathematics, the binary logarithm (log 2 n) is the power to which the number 2 must be raised to obtain the value n.That is, for any real number x, = =. For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5.
On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate results, before the final value is shown. [1] [2] [3] On an expression or formula calculator, one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression.