A computational procedure for reducing a set of (m × m) linear equations Axv = bv to the form MAxv = Mb,v where MAv = Uv is an upper triangular matrix. The variables of the solution vector are found by solving the resulting triangular system for one variable in the last equation, and back-substituting in the next to last equation, and so on. Some form of elimination is central to the simplex method for solving linear-programming problems. Matrices and matrix algebra; Simplex method.
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© 2001 Kluwer Academic Publishers
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Gass, S.I., Harris, C.M. (2001). Gaussian elimination. In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_376
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DOI: https://doi.org/10.1007/1-4020-0611-X_376
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Publisher Name: Springer, New York, NY
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