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Linearizations of rational matrices from general representations
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NSTL
Elsevier
We construct a new family of linearizations of rational matrices R(λ) written in the general form R(λ)=D(λ)+C(λ)A(λ)?1B(λ), where D(λ), C(λ), B(λ) and A(λ) are polynomial matrices. Such representation always exists and is not unique. The new linearizations are constructed from linearizations of the polynomial matrices D(λ) and A(λ), where each of them can be represented in terms of any polynomial basis. In addition, we show how to recover eigenvectors, when R(λ) is regular, and minimal bases and minimal indices, when R(λ) is singular, from those of their linearizations in this family.
Block minimal bases pencilGradeLinearization at infinityLinearization in a setRational eigenvalue problemRational matrixRecovery of eigenvectorsRecovery of minimal basesRecovery of minimal indices
Perez J.、Quintana M.C.
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Department of Mathematical Sciences University of Montana
Department of Mathematics and Systems Analysis Aalto University
NSTL
Elsevier
