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Real NormReducing Shears
Complex NormReducing Shears
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approximation assumed for finite backward perturbation bijna chapter complex conjugate condition number consider converges to normality corresponding coscp departure of diagonal departure of normality diagonal blocks diagonal elements diagonal form diagonalizing representative equal to zero error analysis estimate Euclidean norm Euclidean parameters x,y,z floating-point forward perturbation gonal Hence Hermitean holds hyperbola i,m)-restriction infimum intersection Jacobi Jacobi-like Jacobi-parameters lemma minimize non-singular non-singular matrix norm-reducing process norm-reducing shear transformation normal matrix notations numerically stable obtained optimal norm-reducing shears orthogonal matrix orthogonal shear perturbation F pivot-pair i,m pivot-strategy pre-treatment Proof quartic equation Re(a real matrix rounding errors row congruent Schur's lemma sequence shear matrices shear Q similarity transformations sincp skew-Hermitean small relatively stability bound stable representative stationary point T-partition theorem transformed matrix turbation U*AU unimodular optimal norm-reducing unitary matrix unitary shear vector wordt Zm Zm Zm