Abstract
This paper presents a computer-assisted procedure to prove the invertibility of a linear operator which is the sum of an unbounded bijective and a bounded operator in a Hilbert space, and to compute a bound for the norm of its inverse. By using some projection and constructive a priori error estimates, the invertibility condition together with the norm computation is formulated as an inequality based upon a method originally developed by the authors for obtaining existence and enclosure results for nonlinear partial differential equations. Several examples which confirm the actual effectiveness of the procedure are reported.
| Original language | English |
|---|---|
| Pages (from-to) | 6363-6374 |
| Number of pages | 12 |
| Journal | Journal of Differential Equations |
| Volume | 260 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 2016 Apr 5 |
| Externally published | Yes |
Keywords
- Differential operators
- Numerical verification
- Solvability of linear problem
ASJC Scopus subject areas
- Analysis
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Watanabe, Y., Nagatou, K., Plum, M., & Nakao, M. T. (2016). Norm bound computation for inverses of linear operators in Hilbert spaces. Journal of Differential Equations, 260(7), 6363-6374. https://doi.org/10.1016/j.jde.2015.12.041