A determinant identity and its application in evaluating frequency response matrics
SIAM Journal on Matrix Analysis and Applications
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
LAPACK's user's guide
Algorithm 640: Efficient calculation of frequency response matrices from state space models
ACM Transactions on Mathematical Software (TOMS) - The MIT Press scientific computation series
ACM Transactions on Mathematical Software (TOMS)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
On computing givens rotations reliably and efficiently
ACM Transactions on Mathematical Software (TOMS)
The Shifted Hessenberg System Solve Computation
The Shifted Hessenberg System Solve Computation
Efficient scaling for complex division
ACM Transactions on Mathematical Software (TOMS)
Solving Real Linear Systems with the Complex Schur Decomposition
SIAM Journal on Matrix Analysis and Applications
Shifted Kronecker Product Systems
SIAM Journal on Matrix Analysis and Applications
$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
SIAM Journal on Matrix Analysis and Applications
Efficient generalized Hessenberg form and applications
ACM Transactions on Mathematical Software (TOMS)
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In this article, we propose a numerical algorithm for efficient and robust solution of a sequence of shifted Hessenberg linear systems. In particular, we show how the frequency response &calG;(σ) = d-C(A-σ I)-1b in the single input case can be computed more efficiently than with other state-of-the-art methods. We also provide a backward stability analysis of the proposed algorithm.