Numerical linear algebra
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm
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- enNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm
- Has abstract
- enNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm is as efficient as possible. Numerical linear algebra aims to solve problems of continuous mathematics using finite precision computers, so its applications to the natural and social sciences are as vast as the applications of continuous mathematics. It is often a fundamental part of engineering and computational science problems, such as image and signal processing, telecommunication, computational finance, materials science simulations, structural biology, data mining, bioinformatics, and fluid dynamics. Matrix methods are particularly used in finite difference methods, finite element methods, and the modeling of differential equations. Noting the broad applications of numerical linear algebra, Lloyd N. Trefethen and David Bau, III argue that it is "as fundamental to the mathematical sciences as calculus and differential equations", even though it is a comparatively small field. Because many properties of matrices and vectors also apply to functions and operators, numerical linear algebra can also be viewed as a type of functional analysis which has a particular emphasis on practical algorithms. Common problems in numerical linear algebra include obtaining matrix decompositions like the singular value decomposition, the QR factorization, the LU factorization, or the eigendecomposition, which can then be used to answer common linear algebraic problems like solving linear systems of equations, locating eigenvalues, or least squares optimisation. Numerical linear algebra's central concern with developing algorithms that do not introduce errors when applied to real data on a finite precision computer is often achieved by iterative methods rather than direct ones.
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- Alan Turing
- Algorithmic efficiency
- Algorithms
- Alston Scott Householder
- Analytica (software)
- Arnoldi iteration
- Basic Linear Algebra Subprograms
- Basis (linear algebra)
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- C (programming language)
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- Category:Numerical linear algebra
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- Conjugate gradient method
- Continuous function
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- Diagonal matrix
- Differential equation
- Eigendecomposition
- Eigenvalues
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- Finite difference method
- Finite element method
- Floating-point arithmetic
- Fluid dynamics
- Fortran
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- Generalized minimal residual method
- George Forsythe
- Gram–Schmidt process
- Heinz Rutishauser
- Herman Goldstine
- Householder transformation
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- Irrational number
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- James H. Wilkinson
- John von Neumann
- Krylov subspace
- Lanczos algorithm
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- Linear algebra
- Linear least-squares
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- Lloyd N. Trefethen
- LU factorization
- Maple (software)
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- Numerical methods for linear least squares
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- QR algorithm
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- Signal processing
- Significant digits
- Singular value decomposition
- Singular values
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- Sparse matrix
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- Triangular matrix
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- Álgebra lineal numérica
- Álgebra linear numérica
- Aljabar linear numerik
- Aljabar linear numerik
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- Numerical linear algebra
- Numerical linear algebra
- Numerical linear algebra
- Numerička linearna algebra
- Numerische lineare Algebra
- Numerisk linjär algebra
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- 数値線形代数
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