Our researchers Nenad Mijić, Abhiram Kaushik, Dario Zivkovic and Davor Davidovic have developed a new way to handle one of the trickiest problems in scientific computing: working with huge, unstable datasets that normally break traditional math methods.

Many modern technologies - like climate simulations, medical imaging, AI, and engineering - depend on something called QR factorization, a mathematical tool for solving complex systems of equations. But when the data is extremely unbalanced or “ill-conditioned,” even powerful computers struggle to process it correctly.

This new research introduces an improved algorithm designed specifically for supercomputers with many GPUs working in parallel. The method builds on a fast technique called CholeskyQR and reinforces it with extra stability checks so it doesn’t fall apart when the data is difficult.

The results are impressive:

- It stays accurate even with extremely unstable datasets.

- It runs up to 12× faster than widely used scientific libraries.

- It scales extremely well across many GPUs at once.

In simple terms:

The team found a way to make supercomputers crunch huge, messy datasets much more efficiently - unlocking better performance for simulations, modelling, and scientific discoveries across many fields.

Published in journal MDPI Mathematics

📄Read the full paper here: https://doi.org/10.3390/math13223608

This research was supported by the Hrvatska zaklada za znanost (Croatian Science Foundation) through project HybridScale, and by ERC grants GlueSatLight and YoctoLHC - special thanks to SRCE for providing access to the Supek supercomputer.