| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Outline of Final Research Achievements |
We developed a new type of Tikhonov regularization combined with the theory of reproducing kernels. Using our method of regularization we have challenged some famous and historically difficult inverse problems. Furthermore we constructed concrete algorithms for solving those problems and confirmed their effectiveness by numerical experiments.
In practice, we have studied the following problems: 1) explicit solution of inverse problem in wave equation, 2) solution of Dirichlet problem with arbitrary boundary shape, 3) new discretization method for solving regularized integral equation, 4) method for separating and extracting mixed signal with complex Gabor wavelet transform, 5) validity of our algorithm for constructing of approximate solution of Poisson equation, 6) expansion of reproducing kernel space for inverse problem of heat conduction.
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