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Selected Results from Algebra and Mathematical Optimization,Positive semidefinite matrices will be used extensively throughout the book. Therefore we fix notation here and present some basic properties needed later on.
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Optimization of Polynomials in Non-Commuting Variables978-3-319-33338-0Series ISSN 2191-8198 Series E-ISSN 2191-8201
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Detecting Sums of Hermitian Squares,e we explained basic relations between SOHS polynomials and positive semidefinite Gram matrices. In this chapter we will enclose these results into the Gram matrix method and refine it with the Newton chip method.
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Eigenvalue Optimization of Polynomials in Non-commuting Variables,if it yields a positive semidefinite matrix when we replace the letters (variables) in the polynomial by symmetric matrices of the same order. Helton’s Theorem 1.30 implies that positive semidefinite polynomials are exactly the SOHS polynomials, the set of which we denoted by ...
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Trace Optimization of Polynomials in Non-commuting Variables,c polynomial . trace-positive?” we proposed a relaxation of the problem, i.e., we are asking if . is cyclically equivalent to SOHS. The tracial Gram matrix method based on the tracial Newton polytope was proposed (see Sects. 3.3 and 3.4) to efficiently detect such polynomials.
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Sabine Burgdorf,Igor Klep,Janez Povhpoken input, analyses and translates it, and finally utters the translation. The multilingual system handles dialogs in three business-oriented domains, with context-sensitive translation between three languages (German, English, and Japanese). Since Verbmobil emphasizes the robust processing of spo
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