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An improved incremental SVD and its applications
*½²×ùÄÚÈÝ¼ò½é£ºIn 2002 an incremental singular value decomposition (SVD) was proposed by Brand to efficiently compute the SVD of a matrix. The algorithm needs to evaluate thousands or millions of orthogonal matrices and to multiply them together. Rounding error may destroy the orthogonality. Hence many reorthogonalization steps are needed in practice. In [Linear Algebra and its Applications 415 (2006) 20¨C30], Brand said: It is an open question how often this is necessary to guarantee a certain overall level of numerical precision.'' In this talk, we answer this question: by modifying the algorithm we can avoid computing the most of those orthogonal matrices and hence the reorthogonalizations are not necessary. We prove that the modification does not change the outcome of Brand's algorithm. We have successfully applied our improved scheme to snapshot-based POD model order reduction, time fractional PDEs and integro-differential equations and time dependent optimal control problems. Numerical analysis and experiments are presented to illustrate the impact of our modified incremental SVD on these important problems.