Gaussian Elimination and LU-Decomposition
نویسنده
چکیده
Solving a set of linear equations arises in many contexts in applied mathematics. At least until recently, a claim could be made that solving sets of linear equations (generally as a component of dealing with larger problems like partial-differential-equation solving, or optimization, consumes more computer time than any other computational procedure. (Distant competitors would be the Gram-Schmidt process and the fast Fourier transform computation, and the Gram-Schmidt process is a first cousin to the Gaussian elimination computation since both may be used to solve systems of linear equations, and they are both based on forming particular linear combinations of a given sequence of vectors.) Indeed, the invention of the electronic digital computer was largely motivated by the desire to find a labor-saving means to solve systems of linear equations [Smi10].
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