What does this research mean for the field?

Lipschitz continuous functions can be evaluated rapidly with a maximum relative error arbitrarily close to 2 epsilon using an optimized piecewise Chebyshev approximation algorithm that minimizes rounding errors and cache loading times. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To develop a code generation algorithm for rapid evaluation of Lipschitz continuous functions using piecewise Chebyshev approximation.

May 28, 2026ACM Transactions on Mathematical Software

Algorithm 1XXX: Code generation for piecewise Chebyshev approximation

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Authors

JWJoachim Wuttke AKAlexander Kleinsorge

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Overview

Randomized trial demonstrates rapid evaluation of Lipschitz functions using Chebyshev approximation, suggesting efficient computation techniques.

Key Points

To develop a code generation algorithm for rapid evaluation of Lipschitz continuous functions using piecewise Chebyshev approximation.
Implemented piecewise polynomial approximation to evaluate Lipschitz functions more efficiently.
Analyzed truncation and rounding errors to ensure minimal maximum relative error.
Developed code generation and target algorithms in an open-source project, ppapp.
Achieved a maximum relative error as close to 2ε as desired, with issues near zeros of f.
Minimized cache loading times through coefficient alignment.
Successfully implemented in three real-valued functions within libcerf.

Cite This Study

Wuttke et al. (2026) studied this question.

synapsesocial.com/papers/6a17dbbe3fad632b0f9d8668 https://doi.org/10.1145/3805698

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May 28, 2026ACM Transactions on Mathematical Software

Algorithm 1XXX: Code generation for piecewise Chebyshev approximation

View Full Paper

Ask AI

Bookmark

Authors

JWJoachim Wuttke AKAlexander Kleinsorge

Discussion

Member takes

Overview

Randomized trial demonstrates rapid evaluation of Lipschitz functions using Chebyshev approximation, suggesting efficient computation techniques.

Key Points

To develop a code generation algorithm for rapid evaluation of Lipschitz continuous functions using piecewise Chebyshev approximation.
Implemented piecewise polynomial approximation to evaluate Lipschitz functions more efficiently.
Analyzed truncation and rounding errors to ensure minimal maximum relative error.
Developed code generation and target algorithms in an open-source project, ppapp.
Achieved a maximum relative error as close to 2ε as desired, with issues near zeros of f.
Minimized cache loading times through coefficient alignment.
Successfully implemented in three real-valued functions within libcerf.

Cite This Study

Wuttke et al. (2026) studied this question.

synapsesocial.com/papers/6a17dbbe3fad632b0f9d8668 https://doi.org/10.1145/3805698

View Full Paper

Ask AI

Bookmark