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math.NA2025
Iterative inversion schemes for the Born series and the reduced inverse Born series
Akari Ishida, Manabu Machida
Nonlinear inverse problems have complicated landscapes. Hence the calculation with naive iterative schemes (e.g., Gauss-Newton or conjugate gradients) is trapped in local minima. T…
math.NA2025
Shape optimization for piecewise parameter identification in inverse diffusion problems with a single boundary measurement
Manabu Machida, Hirofumi Notsu, Julius Fergy Tiongson Rabago
This paper proposes a unified shape and coefficient optimization approach for inverse problems governed by diffusion equations. The associated forward problem is considered with a…