Numerical inversion of causative Wiener-Hopf operators and the digital- filter method for inverse problems of heat conduction. (English. Russian original) Zbl 0817.65148
Comput. Math. Math. Phys. 33, No. 11, 1409-1426 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 11, 1603-1625 (1993).
Summary: Stable numerical algorithms are constructed for the inversion of causative and truncated causative Wiener-Hopf operators of the first kind involving computations in the algebras of circulant and triangular Toeplitz matrices. Examples of the implementation of the algorithms and their application to inverse problems of heat conduction are given.
MSC:
65R20 | Numerical methods for integral equations |
65R30 | Numerical methods for ill-posed problems for integral equations |
45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
35R30 | Inverse problems for PDEs |