## Fast Toeplitz orthogonalizations |

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Algorithm 5.2 algorithm is stable applied approximately BBH algorithm BBH method BBH(Q better numerical properties Chapter Cholesky factorization column of Q computes the QR computing Q condition number cos0 Cybenko denoted diagonal downdating problem downdating scheme error curve Example 2.1 Example 4.3 factorization downdating Fast Toeplitz Orthogonalizations flops Givens rotations gives hand side vector Householder transformation Hybrid algorithm ill-conditioned Kailath kth column lattice algorithm least squares problem Levinson's algorithm linear least squares linear prediction problems Math nonsingular norm downdating normal equations orthogonal factor orthogonal matrix orthogonal triangularization plane rotations positive definite principal submatrix procedures Stagel QR decomposition Recursion of Q relative error Results for Example right hand side rithm rk+1 rn+1 row recursion SIAM sin0 singular value square Toeplitz Stage2 Sweet's algorithm Sweet(7 symmetric and positive Table thesis Toeplitz least squares Toeplitz matrix Toeplitz systems Trench's algorithm triangular factor triangular system upper triangular matrix