Titlebook: Inequalities: Theory of Majorization and Its Applications; Albert W. Marshall,Ingram Olkin,Barry C. Arnold Book 2011Latest edition Springe

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Albert W. Marshall,Ingram Olkin,Barry C. Arnoldg., turbo and LDPC codes) from a unified pointof view. Since constrained coding is widely used in magnetic andoptical storage, it is necessary to use some special techniques(modified concatenation scheme or bit insertion) in order to applysoft iterative decoding. .Recent breakthroughs in the design

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Albert W. Marshall,Ingram Olkin,Barry C. Arnoldand LDPC codes) from a unified pointof view. Since constrained coding is widely used in magnetic andoptical storage, it is necessary to use some special techniques(modified concatenation scheme or bit insertion) in order to applysoft iterative decoding. .Recent breakthroughs in the design and decodi

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978-1-4939-3827-8Springer Science+Business Media, LLC 2011

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Inequalities: Theory of Majorization and Its Applications978-0-387-68276-1Series ISSN 0172-7397 Series E-ISSN 2197-568X

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Introductioncomponents of a vector.. Not surprisingly, the notion 4 arises in a variety of contexts, and it can be made precise in a number 5 of ways. But in remarkably many cases, the appropriate precise state- 6 ment is that “.is majorized by.” (written.and defined ahead 7 in Definition A.1). Some of these cases are reviewed here.

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Geometric Inequalitiesgly large. Bottema, Djordjević, Janić, Mitrinović, and Vasić (1969), in their book ., have collected approx- imately 400 inequalities for the triangle. It is shown in this chapter 5 that majorization provides a unified approach to obtaining many known geometric inequalities. This unification also has the advantage of suggesting new inequalities.

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Numerical Analysistion number and norm of a matrix. Both (i) and (ii) depend on a relation between unitarily invariant norms and symmetric gauge functions (see 3.I.1) obtained by von Neumann (1937). Majorization arises from the fact that symmetric gauge functions are Schur-convex.