Colloquium

Colloquium
A complex singular value decomposition algorithm based on the Riemannian Newton method 佐藤寛之 12月6日(金) 13時30分 In this talk, the problem of finding the singular value decomposition of a complex matrix is formulated as an optimization problem on the product of two complex Stiefel manifolds. A new algorithm for the complex singular value decomposition is proposed on the basis of the Riemannian Newton method. This algorithm can provide the singular vectors associated with an arbitrary number of the singular values from the largest one down to a smaller one. Furthermore, once a sufficiently accurate approximate complex SVD is given, the Riemannian Newton method can improve it to be as accurate as the computer accuracy permits.

A complex singular value decomposition algorithm based on the Riemannian Newton method

佐藤寛之

12月6日(金) 13時30分

In this talk, the problem of finding the singular value decomposition of a complex matrix is formulated as an optimization problem on the product of two complex Stiefel manifolds. A new algorithm for the complex singular value decomposition is proposed on the basis of the Riemannian Newton method. This algorithm can provide the singular vectors associated with an arbitrary number of the singular values from the largest one down to a smaller one. Furthermore, once a sufficiently accurate approximate complex SVD is given, the Riemannian Newton method can improve it to be as accurate as the computer accuracy permits.