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MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
It provides a rich Excel-like user interface and its built-in vector programming language FPScript has a syntax similar to MATLAB. FreeMat, an open-source MATLAB-like environment with a GPL license. GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command-line interface for solving ...
LLVM-GCC has included this function since version 1.5 in June 2005. [16] In the C++ Standard Library, the bit-array data structure bitset has a count() method that counts the number of bits that are set. In C++20, a new header <bit> was added, containing functions std::popcount and std::has_single_bit, taking arguments of unsigned integer types.
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.
The input for the method is a continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing within the interval). Each iteration performs these steps: Calculate c, the midpoint of the interval, c = a + b / 2 .
Octave programs consist of a list of function calls or a script. The syntax is matrix-based and provides various functions for matrix operations. It supports various data structures and allows object-oriented programming. [25] Its syntax is very similar to MATLAB, and careful programming of a script will allow it to run on both Octave and ...
Steffensen's method has the drawback that it requires two function evaluations per step, whereas the secant method requires only one evaluation per step, so it is not necessarily most efficient in terms of computational cost, depending on the number of iterations each requires. Newton's method also requires evaluating two functions per step ...
Spaces within a formula must be directly managed (for example by including explicit hair or thin spaces). Variable names must be italicized explicitly, and superscripts and subscripts must use an explicit tag or template. Except for short formulas, the source of a formula typically has more markup overhead and can be difficult to read.