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Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Application of Linearization and Approximation01:29

Application of Linearization and Approximation

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A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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Methods of Medium Optimization01:28

Methods of Medium Optimization

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Optimizing growth media enhances microbial proliferation and maximizes product yield. Statistical experimental design methodologies provide structured and reproducible approaches, offering progressively higher levels of robustness and efficiency.The One-Factor-at-a-Time (OFAT) MethodThe One-Factor-at-a-Time (OFAT) method involves adjusting a single variable while keeping all others constant. However, it cannot detect interactions between variables, often leading to suboptimal outcomes when...
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Related Experiment Video

Updated: Apr 18, 2026

Author Spotlight: Investigating the Mechanism of Action of Acupotomy in Treating Knee Osteoarthritis
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Author Spotlight: Investigating the Mechanism of Action of Acupotomy in Treating Knee Osteoarthritis

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Efficient Boys function evaluation using minimax approximation.

Rasmus Vikhamar-Sandberg1,2, Michal Repisky1,2

  • 1Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, SK-84215 Bratislava, Slovakia.

The Journal of Chemical Physics
|April 17, 2026
PubMed
Summary

We developed an efficient Boys function evaluation algorithm for GPUs. This method uses rational approximations and recurrence relations, optimizing performance for high-throughput computing architectures.

Related Experiment Videos

Last Updated: Apr 18, 2026

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Area of Science:

  • Computational Physics
  • Numerical Analysis

Background:

  • Boys functions are crucial in computational quantum chemistry and physics.
  • Efficient evaluation is needed for modern high-throughput computing architectures, especially GPUs.
  • Existing methods can be inefficient due to data movement costs.

Purpose of the Study:

  • To present a novel algorithm for efficient Boys function evaluation.
  • To tailor the algorithm for modern computing architectures like GPUs.
  • To achieve high accuracy with optimized computational performance.

Main Methods:

  • Combining rational minimax approximations with upward and downward recurrence relations.
  • Partitioning the non-negative real axis into three regions for distinct approximation strategies.
  • Utilizing the rational Remez algorithm for generating minimax coefficients.
  • Avoiding lookup tables and irregular memory access patterns.

Main Results:

  • The algorithm is well-suited for hardware with high throughput and low latency.
  • Achieved a target maximum absolute error of \( \epsilon_{tol} = 5 \times 10^{-14} \).
  • Provided approximation regions and coefficients for Boys functions F0 to F32 in Appendix D.

Conclusions:

  • The proposed algorithm offers an efficient and accurate method for Boys function evaluation.
  • The approach is optimized for modern parallel computing architectures, reducing data movement overhead.
  • This work facilitates faster and more reliable computations in fields relying on Boys functions.