Exploiting mixed-precision redundancy for soft-error detection in LU decomposition

Abstract Mixed-precision arithmetic, widely adopted for performance, creates an overlooked opportunity for fault tolerance. Our mixed-precision panel factorization () algorithm already computes each LU panel in both and ; we show that this inherent redundancy enables soft-error detection at negligible additional cost. We propose four complementary detectors that compare checksum sketches of the two factorizations: (thresholded checksum discrepancy), (outlier analysis of per-row differences), (a randomized-probe combination of both with separate $$L$$ L - and $$U$$ U -factor checks), and (a lightweight cross-check inspired by algorithm-based fault tolerance). Experimental evaluation shows that and achieve high sensitivity with low false-positive rates, while maintains near-zero false positives with moderate sensitivity and complementary coverage for challenging significand-bit faults. Bit-level analysis confirms reliable detection of exponent- and sign-bit errors, with sensitivity decreasing gracefully for low-order significand bits whose perturbations approach the rounding floor. A lightweight panel-fingerprint mechanism extends protection beyond the factorization loop, closing the temporal gap before the triangular solve with guaranteed detection of any single-element corruption and zero false positives. The approach requires only linear work and constant storage per panel, preserving the cubic scaling of standard LU decomposition.