We consider the matrix polynomial P(λ) = Σli= 0Aiλi, with given coeficients Ai 2 C n×n. A matrix S 2 Cn× is called a solvent if P(S) = 0. We explore some approaches to the symbolic and numeric computation of solvents. In particular, we compute formulas for the condition number and backward error of the problem which rely on the contour integral based representation of P(S). Finally, we describe a possible approach for computing exact solvents symbolically.
Some Ideas for the Computation of Matrix Solvents
Boito P.;
2014-01-01
Abstract
We consider the matrix polynomial P(λ) = Σli= 0Aiλi, with given coeficients Ai 2 C n×n. A matrix S 2 Cn× is called a solvent if P(S) = 0. We explore some approaches to the symbolic and numeric computation of solvents. In particular, we compute formulas for the condition number and backward error of the problem which rely on the contour integral based representation of P(S). Finally, we describe a possible approach for computing exact solvents symbolically.File in questo prodotto:
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