Optimal Piecewise Linear Function Approximation for GPU-Based Applications.

Area of Science:

• Computer Science
• Applied Mathematics

Background:

• Evaluating complex mathematical functions is computationally expensive for real-time applications.
• Existing piecewise-polynomial approximations often lack efficiency and practicality.

Purpose of the Study:

• To develop a novel, efficient, and practical technique for evaluating complex, continuous mathematical functions.
• To provide accurate error analysis for piecewise linear approximations.

Main Methods:

• Proposed a new method using two types of piecewise linear approximations for function evaluation.
• Developed a thorough error analysis providing asymptotically tight bounds.
• Implemented the technique on graphics processing units (GPUs) leveraging texture units.

Main Results:

• Achieved a nearly optimal design for piecewise linear approximations with a large budget of subintervals.
• The error analysis offers improved estimates and user control over the error-approximation tradeoff.
• Demonstrated superior performance over existing methods on GPUs, particularly for the Gaussian function.

Conclusions:

• The proposed technique significantly reduces computational cost for evaluating complex functions.
• It enables real-time performance in applications like computer vision and cybernetics.
• The method provides a practical and efficient solution for approximating continuous functions.