Abstract
We consider the numerical solution of a c-stable linear equation in the tensor product space Rn1×...×nd, arising from a discretized elliptic partial differential equation in Rd. Utilizing the stability, we produce an equivalent d-stable generalized Stein-like equation, which can be solved iteratively. For large-scale problems defined by sparse and structured matrices, the methods can be modified for further efficiency, producing algorithms of O(∑ini)+O(ns) computational complexity, under appropriate assumptions (with ns being the flop count for solving a linear system associated with Ai-γIni). Illustrative numerical examples will be presented.
Original language | English |
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Article number | e2106 |
Number of pages | 18 |
Journal | Numerical Linear Algebra with Applications |
Volume | 24 |
Issue number | 6 |
DOIs | |
Publication status | Published - Dec 2017 |
Keywords
- Cayley transform
- Elliptic partial differential equation
- Kronecker product
- Large-scale problem
- Linear equation
- Stein equation
- Sylvester equation