Heinz mean (original) (raw)
In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia as: with 0 ≤ x ≤ 1/2. For different values of x, this Heinz mean interpolates between the arithmetic (x = 0) and geometric (x = 1/2) means such that for 0 < x < 1/2: The Heinz means appear naturally when symmetrizing -divergences. The Heinz mean may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula.
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| dbo:abstract | In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia as: with 0 ≤ x ≤ 1/2. For different values of x, this Heinz mean interpolates between the arithmetic (x = 0) and geometric (x = 1/2) means such that for 0 < x < 1/2: The Heinz means appear naturally when symmetrizing -divergences. The Heinz mean may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula. (en) Em matemática, a média de Heinz (nomeada em honra de E. Heinz) de dois números reais não negativos A e B, foi definida por Bhatia como: com 0 ≤ x ≤ 12.Para valores diferentes de x, essa média de Heinz interpola entre a média aritmética (x = 0) e geométrica (x = 1/2) tal que para 0 < x < 12: A média de Heinz também pode ser definida da mesma maneira para as matrizes semidefinidas positivas e satisfaz uma fórmula de interpolação similar. (pt) |
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| dbo:wikiPageWikiLink | dbr:Muirhead's_inequality dbr:Mean dbr:Geometric_mean dbr:Erhard_Heinz dbr:Arithmetic_mean dbc:Means dbr:Positive_semidefinite_matrix dbr:Inequality_of_arithmetic_and_geometric_means dbr:Real_number |
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| dcterms:subject | dbc:Means |
| rdfs:comment | In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia as: with 0 ≤ x ≤ 1/2. For different values of x, this Heinz mean interpolates between the arithmetic (x = 0) and geometric (x = 1/2) means such that for 0 < x < 1/2: The Heinz means appear naturally when symmetrizing -divergences. The Heinz mean may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula. (en) Em matemática, a média de Heinz (nomeada em honra de E. Heinz) de dois números reais não negativos A e B, foi definida por Bhatia como: com 0 ≤ x ≤ 12.Para valores diferentes de x, essa média de Heinz interpola entre a média aritmética (x = 0) e geométrica (x = 1/2) tal que para 0 < x < 12: A média de Heinz também pode ser definida da mesma maneira para as matrizes semidefinidas positivas e satisfaz uma fórmula de interpolação similar. (pt) |
| rdfs:label | Heinz mean (en) Média de Heinz (pt) |
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