1. Fast enclosure for solutions of Sylvester equations.
- Author
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Miyajima, Shinya
- Subjects
- *
ALGORITHMS , *NUMERICAL solutions to equations , *ERROR analysis in mathematics , *MATHEMATICAL bounds , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: Fast algorithms for enclosing solutions of Sylvester equations are proposed. The results obtained by these algorithms are “verified” in the sense that all the possible rounding errors have been taken into account. For developing these algorithms, theories which directly supply error bounds for numerical solutions are established. The proposed algorithms require only operations if A and B are diagonalizable. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms. [Copyright &y& Elsevier]
- Published
- 2013
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