That the Simplex Algorithm (pivoting) revises the scalars on the “Tableau of Detached Coefficients” in the way one computes them with matrix-vector algebra is verified by experience only! The revision formula for i \neq i{0}

with pivot a_{i_{0}, j_{0}} is not written in any textbook as if it is unnecessary. A “Fundamental Theorem of Simplex Algorithm” is due to be proven. Am I right?

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DeleteThat the Simplex Algorithm (pivoting) revises the scalars on the “Tableau of Detached Coefficients” in the way one computes them with matrix-vector algebra is verified by experience only! The revision formula for i \neq i{0}

ReplyDelete\bar{a_{i, j}} = ( a_{i, j}a_{i_{0}, j_{0}} - a_{i, j_{0}}a_{i_{0}, j} ) / a_{i_{0}, j_{0}}

with pivot a_{i_{0}, j_{0}} is not written in any textbook as if it is unnecessary. A “Fundamental Theorem of Simplex Algorithm” is due to be proven. Am I right?