Tarasov, R. P. 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 Keywords:digital-filter method; causative Wiener-Hopf operators of the first kind; Toeplitz matrices; algorithms; inverse problems; heat conduction PDFBibTeX XMLCite \textit{R. P. Tarasov}, Comput. Math. Math. Phys. 33, No. 11, 1603--1625 (1993; Zbl 0817.65148); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 11, 1603--1625 (1993)