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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
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