Peichen Xie

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math.NA2025

Revealing Floating-Point Accumulation Orders in Software/Hardware Implementations

Peichen Xie, Yanjie Gao, Yang Wang +1

Accumulation-based operations, such as summation and matrix multiplication, are fundamental to numerous computational domains. However, their accumulation orders are often undocume…

math.NA2024

Hyb Error: A Hybrid Metric Combining Absolute and Relative Errors

Peichen Xie

Suppose $x$ is an approximation of $y$ . This paper proposes using $\frac{∣ x - y ∣}{1 + ∣ y ∣}$ , named Hyb Error, to measure the error. This metric equals half the harmonic mean of absolut…