Both packages do the same. LSMR is based on the Fong and Saunders algorithm since 2010 (see the document ), and was introduced to scipy quite recently (i.e. version 0.10 and it won before). According to the document, LSMR should converge faster than LSQR, which uses the Page and Saunders algorithm, which has been around for almost 30 years.
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