Concepts inA set of level 3 basic linear algebra subprograms
Basic Linear Algebra Subprograms
Basic Linear Algebra Subprograms (BLAS) is a de facto application programming interface standard for publishing libraries to perform basic linear algebra operations such as vector and matrix multiplication. They were first published in 1979, and are used to build larger packages such as LAPACK. Heavily used in high-performance computing, highly optimized implementations of the BLAS interface have been developed by hardware vendors such as Intel and AMD, as well as by other authors, e.g.
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Linear algebra
Linear algebra is the branch of mathematics concerning finite or countably infinite dimensional vector spaces, as well as linear mappings between such spaces. Such an investigation is initially motivated by a system of linear equations in several unknowns. Such equations are naturally represented using the formalism of matrices and vectors. Linear algebra is central to both pure and applied mathematics.
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Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s.
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Field extension
In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For instance, the set Q(√2) = {a + b√2 | a, b ∈ Q} is the smallest extension of Q which includes every real solution to the equation x = 2.
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Subroutine
In computer science, a subroutine, also termed procedure, function, routine, method, or subprogram, is a part of source code within a larger computer program that performs a specific task and is relatively independent of the remaining code. As the name subprogram suggests, a subroutine behaves in much the same way as a computer program that is used as one step in a larger program or another subprogram.
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Supercomputer
A supercomputer is a computer at the frontline of current processing capacity, particularly speed of calculation. Supercomputers were introduced in the 1960s and were designed primarily by Seymour Cray at Control Data Corporation (CDC), and later at Cray Research.
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Set (mathematics)
A set is a collection of well defined and distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived.
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Algorithm
In mathematics and computer science, an algorithm Listen/ˈælɡərɪðəm/ (originating from al-Khwārizmī, the famous mathematician Muḥammad ibn Mūsā al-Khwārizmī) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
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