Computing Haar Measures

Pauly, Arno; Seon, Dongseong; Ziegler, Martin

doi:10.4230/lipics.csl.2020.34

Cited by 1 publication

(3 citation statements)

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“…The hyperspace of convex compact subsets does satisfy this, and additional, computational closure properties [39]. 5) Space of probability measures [24,44,57] and subspace of Haar measures on compact groups [51]. 6) Spaces of continuous [63, §6.1], of smooth [28], and of integrable functions [29,60]; equipped with operations like (anti or weak) derivative, or trace.…”

Section: More Continuous Data Typesmentioning

confidence: 99%

“…Some of the computable continuous data types from Subsects. 2.5 and 2.6 already have been implemented in ERC: such as polynomial root-finding (in the sense of Example 3) with QR-algorithm and Wilkinson Shift, or matrix Gaussian Elimination (in the sense of Example 4) with full pivoting [50], or analytic functions [58] or compact metric groups [51] or solution operators to selected PDEs [35].…”

Section: Advanced and Upcoming Erc Programsmentioning

confidence: 99%

“…#P 1 -"completeness" of definite integration generalizes from the real unit interval with respect to the Lebesgue measure to a large class of compact metric groups with respect the Haar measure [51]. Akitoshi Kawamura's 2010 breakthrough result [27] similarly characterizes PSPACE via solving 1D smooth ordinary differential equations.…”

Section: Computational Complexity Of Continuous Datamentioning

confidence: 99%

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Computer Science for Continuous Data

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Ziegler³

2022

Computer Algebra in Scientific Computing

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Section: More Continuous Data Typesmentioning

confidence: 99%

Section: Advanced and Upcoming Erc Programsmentioning

confidence: 99%

Section: Computational Complexity Of Continuous Datamentioning

confidence: 99%

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