
Arb: Efficient ArbitraryPrecision MidpointRadius Interval Arithmetic
Arb is a C library for arbitraryprecision interval arithmetic using the...
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On the Complexity of the PlantingaVegter Algorithm
We introduce a general toolbox for precision control and complexity anal...
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A fast simple algorithm for computing the potential of charges on a line
We present a fast method for evaluating expressions of the form u_j = ∑...
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Evaluation of Chebyshev polynomials on intervals and application to root finding
In approximation theory, it is standard to approximate functions by poly...
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Integrality and arithmeticity of solvable linear groups
We develop a practical algorithm to decide whether a finitely generated ...
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On Differentially Algebraic Generating Series for Walks in the Quarter Plane
We refine necessary and sufficient conditions for the generating series ...
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Interval Algorithm for Random Number Generation: Information Spectrum Approach
The problem of exactly generating a general random process (target proce...
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Rounding Error Analysis of Linear Recurrences Using Generating Series
We develop a toolbox for the error analysis of linear recurrences with constant or polynomial coefficients, based on generating series, Cauchy's method of majorants, and simple results from analytic combinatorics. We illustrate the power of the approach by several nontrivial application examples. Among these examples are a new worstcase analysis of an algorithm for computing Bernoulli numbers, and a new algorithm for evaluating differentially finite functions in interval arithmetic while avoiding interval blowup.
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