In the fi eld of scienti c computation, the orthogonal iteration plays an essential role in computing the invariant subspace corresponding to the largest k eigenvalues. In this paper, we construct a flow that connects the sequence of matrices generated by the orthogonal iteration. Such a flow is called an orthogonal ow. Besides, we also show that the orthogonal iteration forms a time-one mapping of the orthogonal flow. By using a suitable change of variables, the orthogonal flow can be transformed into a Riccati differential equation (RDE). Conversely, an RDE also can be transformed into a flow that can be represented by the orthogonal flow multiplied by an orthogonal matrix.
|Effective start/end date||2019/08/01 → 2020/07/31|
- orthogonal iteration
- invariant subspace
- orthogonal flow
- Riccati differential equation (RDE)
Explore the research topics touched on by this project. These labels are generated based on the underlying awards/grants. Together they form a unique fingerprint.