A note on shifted Hessenberg systems and frequency response computation
ACM Transactions on Mathematical Software (TOMS)
A new digital image watermarking scheme based on Schur decomposition
Multimedia Tools and Applications
Numerical analysis of rational processes beyond Markov chains
Performance Evaluation
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If the complex Schur decomposition is used to solve a real linear system, then the computed solution generally has a complex component because of roundoff error. We show that the real part of the computed solution that is obtained in this way solves a nearby real linear system. Thus, it is “numerically safe” to obtain real solutions to real linear systems via the complex Schur decomposition. This result is useful in certain Kronecker product situations where fast linear equation solving is made possible by reducing the involved matrices to their complex Schur form. This is critical because in these applications one cannot work with the real Schur form without greatly increasing the volume of work.