QR-RLSAlgorithmCyShimabukuroEE491D05-13-05OverviewWhatisQR-putationSimulationResultsQR-RLS?QR-,butthenumericalstablility How? proceedsbyorthogonalsimilaritytransforms. p. --SchmidtAmethodoforthogonalizingasetofvectorsThismethodisnumericallyUnstableThevectorsaren’- posed:whereQT=Hn…=bistransformedintotheeasy-to-solveHouseholderPropertiesitfollows:Symmetrical:Q=Q^Titisorthogonal:Q^{-1}=Q^Tthereforeitisalsoinvolutary:Q^2=IByusingtheHouseholdertransformationmethod,ithasmorestabilitythantheGram-SchmidtGivensRotationAnothertransformationtofindQmatrixMethodzerosoutelementinthematrixMostusefulbecause:Don’thavetobuildanewmatrixbutjustmanipulatingoriginalLessworkandzerosoutwhatisneededMuchmoreeasilyparallelized
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