Centered Forms

Ratschek, Helmut

doi:10.1137/0717055

Cited by 52 publications

(18 citation statements)

References 6 publications

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“…When we apply this centered form to produce IID samples from phylogenetic posterior densities over three and four taxa tree spaces we observe a hundred-fold speedup. Higherorder centered forms [9] in conjunction with constraint propagation [19] may further improve the sampler efficiency enough to produce IID posterior samples from five taxa phylogenetic trees with fifteen topologies in seven dimensions.…”

Section: Resultsmentioning

confidence: 99%

An Auto-validating Rejection Sampler for Differentiable Arithmetical Expressions: Posterior Sampling of Phylogenetic Quartets

Sainudiin

2014

Constraint Programming and Decision Making

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Abstract. We introduce an efficient extension of a recently introduced auto-validating rejection sampler that is capable of producing independent and identically distributed (IID) samples from a large class of target densities with locally Lipschitz arithmetical expressions. Our extension is restricted to target densities that are differentiable. We use the centered form, as opposed to the natural interval extension, to get tighter range enclosures of the differentiable multivariate target density using interval extended gradient differentiation arithmetic. By using the centered form we are able to sample one hundred times faster from the posterior density over the space of phylogenetic trees with four leaves (quartets).

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Section: Resultsmentioning

confidence: 99%

An Auto-validating Rejection Sampler for Differentiable Arithmetical Expressions: Posterior Sampling of Phylogenetic Quartets

Sainudiin

2014

Constraint Programming and Decision Making

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“…This was-verified by Hansen [2]. Explicit forms were given by Hansen [2] for polynomials and by Ratschek [8] for rational functions. Forms for functions in k variables were furthermore described by Ratschek-Schroder [7].…”

Section: Introductionmentioning

confidence: 91%

Low complexity k-dimensional centered forms

Rokne

1986

Computing

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--ZusammenfassungLow Complexity k-dimensional Centered Forms. A new method for computing the centered form in k dimensions for polynomials and rational functions is presented. T~le method is not nearly as computationally intensive as the method proposed in Ratschek-Schroder [-7] in that it avoids the calculation of the partial derivatives of the functions. The method is also easier to implement than the slope method proposed by . Some numer.ic~l 'results are given.

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“…±0.009765625 100x1y1δ1 ±0.001953125 monomials using a monomial ζ i along with a constant C i that centers the monomial ζ i over the desired range, for this has previously been shown to obtain the best error properties [50]. …”

Section: Controlling Execution Timementioning

confidence: 99%

A Scalable Precision Analysis Framework

Boland

Constantinides

2013

IEEE Trans. Multimedia

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Abstract-In embedded computing, typically some form of silicon area or power budget restricts the potential performance achievable. For algorithms with limited dynamic range, custom hardware accelerators manage to extract significant additional performance for such a budget via mapping operations in the algorithm to fixed-point. However, for complex applications requiring floating-point computation, the potential performance improvement over software is reduced. Nonetheless, custom hardware can still customise the precision of floating-point operators, unlike software which is restricted to IEEE standard single or double precision, to increase the overall performance at the cost of increasing the error observed in the final computational result. Unfortunately, because it is difficult to determine if this error increase is tolerable, this task is rarely performed.We present a new analytical technique to calculate bounds on the range or relative error of output variables, enabling custom hardware accelerators to be tolerant of floating point errors by design. In contrast to existing tools that perform this task, our approach scales to larger examples and obtains tighter bounds, within a smaller execution time. Furthermore, it allows a user to trade the quality of bounds with execution time of the procedure, making it suitable for both small and large-scale algorithms.

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Centered Forms

Cited by 52 publications

References 6 publications

An Auto-validating Rejection Sampler for Differentiable Arithmetical Expressions: Posterior Sampling of Phylogenetic Quartets

An Auto-validating Rejection Sampler for Differentiable Arithmetical Expressions: Posterior Sampling of Phylogenetic Quartets

Low complexity k-dimensional centered forms

A Scalable Precision Analysis Framework

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