Search results
Results from the WOW.Com Content Network
Classical elimination theory culminated with the work of Francis Macaulay on multivariate resultants, as described in the chapter on Elimination theory in the first editions (1930) of Bartel van der Waerden's Moderne Algebra. After that, elimination theory was ignored by most algebraic geometers for almost thirty years, until the introduction ...
The notes were widely imitated, which made (what is now called) Gaussian elimination a standard lesson in algebra textbooks by the end of the 18th century. Carl Friedrich Gauss in 1810 devised a notation for symmetric elimination that was adopted in the 19th century by professional hand computers to solve the normal equations of least-squares ...
In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as
LU decomposition on Math-Linux. LU decomposition at Holistic Numerical Methods Institute; LU matrix factorization. MATLAB reference. Computer code. LAPACK is a collection of FORTRAN subroutines for solving dense linear algebra problems; ALGLIB includes a partial port of the LAPACK to C++, C#, Delphi, etc. C++ code, Prof. J. Loomis, University ...
Linear algebra is the branch of mathematics concerning linear equations such as: ... Gauss further described the method of elimination, ... To solve them, ...
Elimination theory, the theory of the methods to eliminate variables between polynomial equations. Disjunctive syllogism, a rule of inference; Gaussian elimination, a method of solving systems of linear equations; Fourier–Motzkin elimination, an algorithm for reducing systems of linear inequalities
Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph Fourier [ 1 ] who proposed the method in 1826 and Theodore Motzkin who re-discovered it in 1936.
Comments: The LUP and LU decompositions are useful in solving an n-by-n system of linear equations =. These decompositions summarize the process of Gaussian elimination in matrix form. Matrix P represents any row interchanges carried out in the process of Gaussian elimination.