Solving block low-rank linear systems by LU factorization is numerically stable

Abstract Block low-rank (BLR) matrices possess a blockwise property that can be exploited to reduce the complexity of numerical linear algebra algorithms. The impact these approximations on stability algorithms in floating-point arithmetic has not previously been analysed. We present rounding error analysis for solution system by LU factorization BLR matrices. Assuming stable pivoting scheme is used, we prove backward stability: relative bounded modest constant times $\varepsilon $, where threshold $ parameter controlling accuracy approximations. In addition this key result, our offers three new insights into behaviour First, compare use global or local and find one should preferred. Second, show performing intermediate recompressions during significantly its cost without compromising stability. Third, consider different variants determine update–compress–factor variant best. Tests wide range from various real-life applications predictions are realized practice.