Uppsala University Department of Information Technology

Technical Report 2015-011

Schur Complement Matrix and its (Elementwise) Approximation: A Spectral Analysis Based on GLT Sequences

Ali Dorostkar, Maya Neytcheva, and Stefano Serra-Capizzano

March 2015

Using the notion of the so-called spectral symbol in the Generalized Locally Toeplitz (GLT) setting, we derive the GLT symbol of the sequence of matrices {An} approximating the elasticity equations. Further, as the GLT class defines an algebra of matrix sequences and Schur complements are obtained via elementary algebraic operation on the blocks of An, we derive the symbol fS of the associated sequences of Schur complements {Sn} and that of its element-wise approximation.

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