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Interconversion between charge and spin currents via spin-orbit coupling underpins spin orbitronics. Magnons, which are the quanta of spin waves, can exchange angular momentum with conduction-electron spins through spin-flip scattering, suggesting a direct route for charge-to-magnon conversion. Here, we predict that in single-layer ferromagnets, an applied electric current induces a transverse magnon current, producing electrical magnon Hall and inverse magnon Hall effects that share the symmetry of the spin Hall and inverse spin Hall effects. This effect gives rise to a magnon Hall magnetoresistance in CoFeB and NiFe, with an efficiency comparable to the spin Hall effect and a characteristic decay length on the order of micrometers, far exceeding typical electron spin diffusion lengths. By enabling the direct generation and detection of long-range magnon currents, our findings open new pathways for low-loss, on-chip spin-based logic and energy-harvesting devices. 

ABSTRACT Interpolative decompositions (ID) involve “natural bases” of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. Although finding optimal skeleton subsets is combinatorially hard, classical greedy pivoting algorithms with rank‐revealing properties like column‐pivoted QR (CPQR) often provide good heuristics in practice. To select skeletons efficiently for large matrices, randomized sketching is commonly leveraged as a preprocessing step to reduce the problem dimension while preserving essential information in the matrix. In addition to accelerating computations, randomization via sketching improves robustness against adversarial inputs while relaxing the rank‐revealing assumption on the pivoting scheme. This enables faster skeleton selection based on LU with partial pivoting (LUPP) as a reliable alternative to rank‐revealing pivoting methods like CPQR. However, while coupling sketching with LUPP provides an efficient solution for ID with a given rank, the lack of rank‐revealing properties of LUPP makes it challenging to adaptively determine a suitable rank without prior knowledge of the matrix spectrum. As a remedy, in this work, we introduce an adaptive randomized LUPP algorithm that approximates the desired rank via fast estimation of the residual error. The resulting algorithm is not only adaptive but also parallelizable, attaining much higher practical speed due to the lower communication requirements of LUPP over CPQR. The method has been implemented for both CPUs and GPUs, and the resulting software has been made publicly available.