## Error Analysis of Householder Transformations as Applied to the Standard and Generalized Eigenvalue Problems |

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2t-digit accumulator 2t-digit answer Ai_i ANALYSIS OF HOUSEHOLDER answer is retained application of Householder Applying lemma assumption given B|IE backward error analysis binary digits computed Householder transformation computed Q^Qk-1 computed value computing c given determines the error eigen eigenvalue problem Ax eigenvalue problem determines equation 13 error in computing exact equivalence transformation exact matrix multiplication exact similarity transformation exact unitary similarity floating-point number following equation following sequence given in equation given the vector hermitian Hessenberg form Householder similarity transformation hypothesis indicates an n x n information in reference ith component Langley Research Center mantissa n x n matrix related NASA norm p2_t Parlett ref Performing Organization perturbation matrix postmultiplication premultiplication QZ algorithm ref relative error resulting perturbation matrices scalar sequence of Householder sndoub standard eigenvalue problem symbol t-digit numbers terms of A||E theorem tion transformation with exact unitary similarity transformation Wilkinson ref