ComputingComputer ScienceAlgorithmsOptimizationTheory Of ComputationLinear AlgebraMatrix ComputationNumerical AlgorithmsNumerical AnalysisNumerical Linear AlgebraSingular Perturbation TheoryComputational Matrix TheoryMatrix Perturbation TheoryNumerical RobustnessRobustnessSingular Perturbation Analysis
The author proposes a novel algorithm with enhanced numerical robustness for computing singular perturbation approximations of linear, continuous or discrete systems. This algorithm circumvents the computation of possibly ill-conditioned balancing transformations. Instead, well-conditioned projection matrices are determined for computing state-space representations suitable for applying the singular perturbation formulas. The projection matrices are computed using the Cholesky (square-root) factors of the gramians. The proposed algorithm is intended for efficient computer implementation. It can handle both minimal and nonminimal systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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