![]() QTs(11.6.2)The QR transformation preserves the upper Hessenberg form of the original matrixA ≡ A1, and the workload on such a matrix is O(n2 ) per iteration as opposedto O(n3 ) on a general matrix.(As − ks 1) = Rs(11.6.1)where Q is orthogonal and R is upper triangular, andAs+1 = Rs.11.6 The QR Algorithm for Real HessenbergMatricesRecall the following relations for the QR algorithm with shifts:Qs Stoer, J., and Bulirsch, R.ġ980, Introduction to Numerical Analysis (New York: Springer-Verlag),§6.5.4. 6 ofLecture Notes in Computer Science (New York: Springer-Verlag). 1976, Matrix Eigensystem Routines - EISPACK Guide, 2nd ed., vol. II of Handbook for Automatic Computation (New York: Springer-Verlag). 486Chapter 11.Eigensystems}}CITED REFERENCES AND FURTHER READING:Wilkinson, J.H., and Reinsch, C.
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