The fast solution of least squares problems and its applications.

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04768
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Computational science
• Research Institution: National Institute of Informatics
• Principal Investigator: Hayami Ken 国立情報学研究所, 情報学プリンシプル研究系, 教授 (20251358)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 最小二乗問題 / クリロフ部分空間法 / 非負制約付き最小二乗問題 / 画像復元 / 非負値行列因子分解 / 線形計画問題 / 共役勾配法 / 主双対内点法

Outline of Final Research Achievements

We developed a method for nonnegative least squares problems by using a modulus transformation which reduces the problem to solving a sequence of unconstrained least squares problems, proved its convergence and showed its superiority. We also applied the method to image restoration problems and showed its effectiveness. Further, we applied it to nonnegative matrix factorization (NMF), which is useful in signal processing etc., and showed its superiority.
We showed that the right preconditioned MINRES method converges without breakdown for least squares problems whose coefficient matrix is symmetric positive semidefinite, and proposed using the Eisenstat-SSOR method for the right preconditioning, and showed its superiority. We applied our inner iteration preconditioned Krylov subspace method to least squares problems arising in each iteration of the primal-dual interior point method for linear programming problems, and showed its effectiveness.

Free Research Field

数値解析