supported by National Science Foundation of USA (Grant Nos. DMS1228271 and DMS-1522587);National Natural Science Foundation of China for Creative Research Groups (Grant No. 11321061);the National Basic Research Program of China (Grant No. 2011CB309703);the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
Partial eigenvalue decomposition(PEVD) and partial singular value decomposition(PSVD) of large sparse matrices are of fundamental importance in a wide range of applications, including latent semantic indexing, spectra...