Improved Backward Error Bounds for LU and Cholesky Factorizations

Assuming standard floating-point arithmetic (in base $\beta$, precision $p$) and barring underflow and overflow, classical rounding error analysis of the LU or Cholesky factorization of an $n\times n$ matrix $A$ provides backward error bounds of the form $|\Delta A| \le \gamma_n |\widehat L| |\wideh...

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