arXiv subjects

Angelika Schwarz

Publications and source records attributed to Angelika Schwarz.

3 recordsLinked to original sources

arXiv2025

Guaranteed DGEMM Accuracy While Using Reduced Precision Tensor Cores Through Extensions of the Ozaki Scheme

The rapid growth of artificial intelligence (AI) has made low-precision formats such as FP16, FP8, and, most recently, block-scaled FP4 the primary focus of modern GPUs, where Tensor Cores now deliver orders-of-magnitude higher throughput than traditional FP64 pipelines. This hardware shift has sparked a new line of algorithm research: using low-precision units to emulate double-precision accuracy through schemes such as Ozaki decompositions. We advance this direction with Automatic Dynamic Precision (ADP), a fully GPU-resident framework that makes emulated FP64 matrix multiplication both efficient and reliable. At its core is the Exponent Span Capacity (ESC), a hardware-agnostic estimator that conservatively determines the decomposition parameter (also known as slices) required to achieve FP64-level accuracy. Built on ESC, ADP integrates exception handling, run time heuristics, and seamless fallback to native FP64, ensuring correctness without host-device synchronization or user intervention. Additionally, we further improve Ozaki-style decompositions with an unsigned integer slicing scheme, which increases representational efficiency and reduces computational waste. Validated against recently proposed BLAS grading tests, ADP consistently preserves FP64 fidelity on challenging inputs while incurring less than 10% run time overhead. In a 55-bit mantissa setting, our approach achieves up to 2.3x and 13.2x speedups over native FP64 GEMM on NVIDIA Blackwell GB200 and the RTX Pro 6000 Blackwell Server Edition, respectively. Our results demonstrate that low-precision accelerators can serve as a practical, production-ready foundation for high-fidelity and high-performance scientific computing workloads.

cs.DC↗

arXiv2021

Robust level-3 BLAS Inverse Iteration from the Hessenberg Matrix

Inverse iteration is known to be an effective method for computing eigenvectors corresponding to simple and well-separated eigenvalues. In the non-symmetric case, the solution of shifted Hessenberg systems is a central step. Existing inverse iteration solvers approach the solution of the shifted Hessenberg systems with either RQ or LU factorizations and, once factored, solve the corresponding systems. This approach has limited level-3 BLAS potential since distinct shifts have distinct factorizations. This paper rearranges the RQ approach such that data shared between distinct shifts is exposed. Thereby the backward substitution with the triangular R factor can be expressed mostly with matrix-matrix multiplications (level-3 BLAS). The resulting algorithm computes eigenvectors in a tiled, overflow-free, and task-parallel fashion. The numerical experiments show that the new algorithm outperforms existing inverse iteration solvers for the computation of both real and complex eigenvectors.

cs.MS↗

arXiv2019

Robust Task-Parallel Solution of the Triangular Sylvester Equation

The Bartels-Stewart algorithm is a standard approach to solving the dense Sylvester equation. It reduces the problem to the solution of the triangular Sylvester equation. The triangular Sylvester equation is solved with a variant of backward substitution. Backward substitution is prone to overflow. Overflow can be avoided by dynamic scaling of the solution matrix. An algorithm which prevents overflow is said to be robust. The standard library LAPACK contains the robust scalar sequential solver dtrsyl. This paper derives a robust, level-3 BLAS-based task-parallel solver. By adding overflow protection, our robust solver closes the gap between problems solvable by LAPACK and problems solvable by existing non-robust task-parallel solvers. We demonstrate that our robust solver achieves a similar performance as non-robust solvers.

cs.MS↗