| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Research Abstract |
In this project, we investigate the perturbations on singular values and the forward errors of the mdLVs variables, which occur in the mdLVs algorithm, through two kinds of error analysis in floating point arithmetic. Therefore the forward stability of the mdLVs algorithm is proved. Next we present a new similarity transformation named the dLV_\infty similarity transformation by considering the case where the discretization parameter \delta(n) goes to infinity in the integrable dLV system. It is proved that the singular values of bidiagonal matrix are computable by using the dLV_\infty transformation repeatedly. Therefore we clarify that the relative perturbations in the singular values are sufficiently small through the mixed forward-backward error analysis. We finally show that the dLV_\infty transformation is forward stable.
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