Concepts inUpdating an LU Factorization with Pivoting
Matrix (mathematics)
In mathematics, a matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements is Matrices of the same size can be added or subtracted element by element. The rule for matrix multiplication is more complicated, and two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second.
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LU decomposition
In linear algebra, LU decomposition (also called LU factorization) factorizes a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. LU decomposition is a key step in several fundamental numerical algorithms in linear algebra such as solving a system of linear equations, inverting a matrix, or computing the determinant of a matrix. It can be viewed as the matrix form of Gaussian elimination.
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Factorization
In mathematics, factorization (also factorisation in British English) or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained.
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Pivot element
The pivot or pivot element is the element of a matrix, an array, or some other kind of finite set, which is selected first by an algorithm, to do certain calculations. In the case of matrix algorithms, a pivot entry is usually required to be at least distinct from zero, and often distant from it; in this case finding this element is called pivoting.
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Numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a desirable property of numerical algorithms. The precise definition of stability depends on the context, but it is derived from the accuracy of the algorithm. An opposite phenomenon is instability.
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Algebra
Algebra (from Arabic al-jebr meaning "reunion of broken parts") is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.
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Application programming interface
An application programming interface (API) is a specification intended to be used as an interface by software components to communicate with each other. An API may include specifications for routines, data structures, object classes, and variables. An API specification can take many forms, including an International Standard such as POSIX or vendor documentation such as the Microsoft Windows API, or the libraries of a programming language, e.g. Standard Template Library in C++ or Java API.
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Intel
Intel Corporation is an American multinational semiconductor chip maker corporation headquartered in Santa Clara, California, United States and the world's largest and highest valued semiconductor chip maker, based on revenue. It is the inventor of the x86 series of microprocessors, the processors found in most personal computers. Intel Corporation, founded on July 18, 1968, is a portmanteau of Integrated Electronics (though a common misconception is that "Intel" is from the word intelligence).
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