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17-04-2020 | Original Paper | Issue 3/2021 Open Access

Numerical Algorithms 3/2021

Two algorithms for the exchange lemma

Numerical Algorithms > Issue 3/2021
Stefan Barańczuk, Bogdan Szydło
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In this note, we present two new algorithms for the Steinitz Exchange Lemma. They are grounded on a single application of a procedure (finding either a row echelon form or a basic minor) that has to be applied repeatedly in previously known algorithms. Proving correctness of both the algorithms, we obtain two new, direct proofs of the Exchange Lemma.
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