“…Let a finite sequence A = (A [k] ) k , where 1 ≤ k ≤ n, of complex 2 × 2 matrices be given, and let the corresponding sequences U = (U [k] ) k , V = (V [k] ) k of 2×2 unitary matrices be sought for, as well as a sequence Σ = (Σ [k] ) k of 2 × 2 diagonal matrices with the real and non-negative diagonal elements, such that A [k] = U [k] Σ [k] (V [k] ) * , i.e., for each k, the right hand side of the equation is the singular value decomposition (SVD) of the left hand side. This batch of 2 × 2 SVD computational tasks arises naturally in, e.g., parallelization of the Kogbetliantz algorithm [1] for the 2n × 2n SVD [2][3][4]. A parallel step of the algorithm, repeated until convergence, amounts to forming and processing such a batch, with each A [k] assembled column by column from the elements of the iteration matrix at the suitably chosen pivot positions (p k , p k ), (q k , p k ), (p k , q k ), and (q k , q k ).…”