Nonnegative Polynomial with no Certificate of Nonnegativity in the Simplicial Bernstein Basis
classification
🧮 math.NA
cs.SY
keywords
bernsteinnonnegativebasiscannotnonnegativitypolynomialsimplicialcertificate
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This paper presents a nonnegative polynomial that cannot be represented with nonnegative coefficients in the simplicial Bernstein basis by subdividing the standard simplex. The example shows that Bernstein Theorem cannot be extended to certificates of nonnegativity for polynomials with zeros at isolated points.
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