Eberly, Wayne2013-05-292013-05-292013-05-29http://hdl.handle.net/1880/49494A simpli ed \block Lanczos" algorithm is presented and its correctness established. While its e ciency in the general case is not proved, preconditioning used for similar algo- rithms is also su cient here. Results concerning reliability and e ciency may be of more general interest because they may serve to (somewhat) better explain the performance of other block algorithms, including block Wiedemann algo- rithms and algorithms that use rectangular blocking.engAlgorithmsPerformanceReliabilityAlgebraic algorithms, analysis of algotithmstechnical report2013-1036-0310.11575/PRISM/30595