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• W2950375897 abstract "Let $A_0, A_1, ldots, A_n$ be given square matrices of size $m$ with rational coefficients. The paper focuses on the exact computation of one point in each connected component of the real determinantal variety ${X inRR^n : :: det(A_0+x_1A_1+cdots+x_nA_n)=0}$. Such a problem finds applications in many areas such as control theory, computational geometry, optimization, etc. Using standard complexity results this problem can be solved using $m^{O(n)}$ arithmetic operations. Under some genericity assumptions on the coefficients of the matrices, we provide an algorithm solving this problem whose runtime is essentially quadratic in ${{n+m}choose{n}}^{3}$. We also report on experiments with a computer implementation of this algorithm. Its practical performance illustrates the complexity estimates. In particular, we emphasize that for subfamilies of this problem where $m$ is fixed, the complexity is polynomial in $n$." @default.
• W2950375897 created "2019-06-27" @default.
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• W2950375897 date "2014-12-18" @default.
• W2950375897 modified "2023-10-01" @default.
• W2950375897 title "Real root finding for determinants of linear matrices" @default.
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• W2950375897 hasPublicationYear "2014" @default.
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