| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| 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.
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