Analysis of Truncation Error of Matrix Low Rank Approximation Algorithm Using QR Decomposition with Pivot Selection

Abstract

Abstract. QR decomposition with pivot selection is known to be less accurate as low rank approximation than singular value decomposition, but it is often used because the calculation amount is smaller than SVD. The minimum upper bound of the truncation error of QR decomposition with pivot selection is estimated accurately in case r = n − 1 of approximating m × n (m ≥ n) matrix to matrix whose rank is r so it is introduced in this paper.