On a Second-order Expansion of the Singular Subspace Decomposition with Application to the Tsvd Solution Sensitivity Technical Report Ref: Tr-pa-13-22
نویسندگان
چکیده
We present a second-order expansion for singular subspace decomposition in the context of real matrices. Furthermore, we show that, when some particular assumptions are considered, the obtained results reduce to existing ones, namely those by Vaccaro [SIAM J. on Matrix Anal. and Appl., 15(1994), pp. 661-671], or those by Zhengyuan [IEEE Trans. Signal Proc., 50(2002), pp. 2820-2830]. We make use of our results to study the second-order sensitivity of the TSVD solution to least-squares problems. Some numerical examples are provided to confirm the theoretical developments of this study.
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