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In computer science, a lookup table (LUT) is an array that replaces runtime computation with a simpler array indexing operation, in a process termed as direct addressing.The savings in processing time can be significant, because retrieving a value from memory is often faster than carrying out an "expensive" computation or input/output operation. [1]
The following list contains syntax examples of how a range of element of an array can be accessed. In the following table: first – the index of the first element in the slice; last – the index of the last element in the slice; end – one more than the index of last element in the slice; len – the length of the slice (= end - first)
Matrices can be defined by separating the elements of a row with blank space or comma and using a semicolon to separate the rows. The list of elements should be surrounded by square brackets []. Parentheses are used to access elements and subarrays (they are also used to denote a function argument list).
Given a list L of n elements with values or records L 0.... L n−1, and target value T, the following subroutine uses linear search to find the index of the target T in L. [3] Set i to 0. If L i = T, the search terminates successfully; return i. Increase i by 1. If i < n, go to step 2. Otherwise, the search terminates unsuccessfully.
On the other hand, if a function's domain is continuous, a table can give the values of the function at specific values of the domain. If an intermediate value is needed, interpolation can be used to estimate the value of the function. For example, a portion of a table for the sine function might be given as follows, with values rounded to 6 ...
The one-form dθ (defined on the complement of the origin) is closed but not exact, and it generates the first de Rham cohomology group of the punctured plane. In particular, if ω is any closed differentiable one-form defined on the complement of the origin, then the integral of ω along closed loops gives a multiple of the winding number.
The value of the function at a critical point is a critical value. [1] More specifically, when dealing with functions of a real variable, a critical point, also known as a stationary point, is a point in the domain of the function where the function derivative is equal to zero (or where the function is not differentiable). [2]
The fixed-point index can be thought of as a multiplicity measurement for fixed points. The index can be easily defined in the setting of complex analysis: Let f(z) be a holomorphic mapping on the complex plane, and let z 0 be a fixed point of f. Then the function f(z) − z is holomorphic, and has an isolated zero at z 0.