Piecewise quadratic interpolation and applications to the Young inequality (Q1682570)
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scientific article; zbMATH DE number 6814111
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Piecewise quadratic interpolation and applications to the Young inequality |
scientific article; zbMATH DE number 6814111 |
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Piecewise quadratic interpolation and applications to the Young inequality (English)
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30 November 2017
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The paper uses piecewise quadratic interpolation to derive refinements and reverses of Young's inequality about weighted geometric means and algebraic means of two positive numbers (Propositions 3.3--3.6). These inequalities are then generalized for positive definite matrices in terms of determinants (Theorem 3.7) and Löwner partial ordering (Theorems 3.8 and 3.9).
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polynomial interpolation
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matrix means
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Young inequality
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geometric means
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algebraic means
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positive definite matrices
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determinant
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Löwner partial ordering
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