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Incremental singular value decomposition (SVD) was proposed by Brand toefficiently compute the SVD of a matrix. The algorithm needs to computethousands or millions of orthogonal matrices and to multiply them together.However, the multiplications may corrode the orthogonality. Hence manyreorthogonalizations are needed in practice. In [Linear Algebra and itsApplications 415 (2006) 20-30], Brand asked "It is an open question how oftenthis is necessary to guarantee a certain overall level of numerical precision;it does not change the overall complexity." In this paper, we answer thisquestion and the answer is we can avoid computing the large amount of thoseorthogonal matrices and hence the reorthogonalizations are not necessary bymodifying his algorithm. We prove that the modification does not change theoutcomes of the algorithm. Numerical experiments are presented to illustratethe performance of our modification.

An answer to an open question in the incremental SVD