正交流於數值方法上之應用

In the field of scientific 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 flow. 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.