## 4 Experiments
Furthermore, they will facilitate direct data transfer between GPUs using technologies like MVAPICH2-GDR 2.0 and OpenMPI 1.8.3, which utilize GPUDirect, will enhance efficiency. Finally, they will apply our algorithm to real-world problems such as electronic structure computations, and Sturm-Liouville problems will demonstrate its practical applicability. A.E.-C.: Software, Validation, Formal Analysis, Investigation, Writing--Original Draft, Writing. J.A.R.-R.: Software, Validation, Formal Analysis, Investigation. A.M.-V.: Conceptualization, Methodology, Software, Validation, Investigation, Writing--Review and Editing, Resources, Project Administration. L.L.B.-S.: Writing--Review and Editing, Funding Acquisition. S.V.C.-V.: Methodology, Validation, Investigation, Funding Acquisition. E.H.-R.: Conceptualization, Methodology, Investigation and Validation. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Data Availability Statement: Data are available from the corresponding authors upon request. The authors declare no conflicts of interest. ## References

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