Lecture on Numerical Linear Algebra: Wei XU博士による高速SVDに関する講演会イベント日時: 03-27
投稿者: 速水 謙(国立情報学研究所) ()
|会場: 国立情報学研究所, 20F, Room 2005 (Lecture Room 1)|
概要: "A Fast SVD for Multi-Level Block Hankel Matrix with Minimal Memory Storage" というタイトルで御講演いただきます
2017年 3月27日 11:00-12:00am
国立情報学研究所(National Institute of Informatics), 20th Floor, Room 2005 (Lecture Room 1),
Dr. Wei XU
Associate Professor, Department of Mathematics, Tongji University, Shanghai
A Fast SVD for Multi-Level Block Hankel Matrix with Minimal Memory Storage
The specially structured Hankel matrices and the general multi-level Block Hankel (MBH) matrices arise in many applications.
For example, in seismic data processing, Cadzow filtering, a well-known method for removing random and coherent noise in seismic records, requires a matrix rank reduction of large complex MBH matrices.
The singular value decomposition (SVD) is a stable method for the rank reduction, however, the standard SVD is computationally intensive.
In this paper, we propose a fast SVD method for MBH matrices by exploiting their special structure.
Our method consists of two stages: bidiagonalization and diagonalization.
First, an MBH matrix $G$ is bidiagonalized, or tridiagonalized when $G$ is square, using the Lanczos method.
Then, a partial SVD of the reduced bidiagonal (tridiagonal) matrix is computed via the twisted factorization method.
The high efficiency of our method is achieved in two ways.
In the Lanczos method in the first stage, we propose a novel fast MBH matrix-vector multiplication, which applies 1-D FFT instead of multi-dimensional FFT and reduces storage requirement, but with similar efficiency.
In the second stage, we adopt a partial SVD method for the rank reduction using the twisted factorization.
Our numerical experiments show that our fast method significantly reduces both the computation and storage requirements.
Our seismic examples indicate that the Cadzow filtering with our fast matrix reduction is efficient in reducing random noise.
Thus, our method is potentially viable for solving large size problems in seismic data processing, and also for other applications where MBH SVD is required.
速水 謙 (Ken Hayami)
〒101-8430 東京都 千代田区 一ツ橋 2-1-2 国立情報学研究所