On The Numerical Computation of Aᵅx=b
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The paper, ODE-based double-preconditioning for solving linear systems A^{\alpha}x = b and f(A)x = b, by Antoine and Lorin [5], introduces different types of precon- ditioners for efficiently computing large sparse systems Ax = b. In this thesis, we introduce the notion of matrix functions f(A) and present several methods for computing p-th root matrices A^(1/p). Finally we propose some algorithms for solving fractional linear systems.
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Copyright © 2020 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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