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References
BACKUS, G. and GILBERT, F., 1968, The resolving power of gross earth data, Geophys. J.R. Astr. Soc., 16, 169–205
BALTES, H.P. (ed.), 1978, Inverse Source Problems in Optics, Topics in Current Physics, Vol 9 (Springer, Berlin)
BALTES, H.P. (ed.), 1980, Inverse Scattering Problems in Optics, Topics in Current Physics, Vol 20 (Springer, Berlin)
BAKUSHINSKII, A.B., 1965, A numerical method for solving Fredholm integral equations of the first kind, USSR Comp. Math. Math.Phys. 5 (No.4), 226–233
BERTERO, M. and VIANO, G.A., 1978, On probabilistic methods for the solution of improperly posed problems, Bollettino U.M.I. 15-B, 483–508
BERTERO, M., 1982, Problemi lineari non ben posti e metodi di regolarizzazione. (Consiglio Nazionale delle Ricerche, Firenze)
BERTERO, M., dE MOL, C. and PIKE, E.R., 1985, Linear inverse problems with discrete data. I: General formulation and singular system analysis, Inverse Problems 1, 301–330
BOERNER, W.M., BRAND, H., CRAM, L.A., GJESSING, T.D., JORDAN, A.K., KEYDEL, W., SCHWIERZ, G. and VOGEL, M. (eds.), 1985, Inverse Methods in Electromagnetic Imaging, Part 1 and Part 2 (Reidel, Dordrecht)
CARASSO, A. and STONE, A.P., (eds.), 1975, Improperly Posed Boundary Value Problems (Pitman Publ., London)
CHADAN, K. and SABATIER, P.C., 1977, Inverse Problems in Quantum Scattering Theory (Springer, Berlin)
CIULLI, S., POMPONIU, C. and SABBA-STEFANESCU, I, 1975, Analytic extrapolation techniques and stability problems in dispersion relation theory, Phys. Reports, 17, 133–224
COLIN, L. (ed.), 1972, Mathematics of Profile Inversion, Proc. of a workshop held at Ames Research Center, Moffat Field, CA 994084, June 12–16, 1971; NASA TM-X-62. 150
COLLI FRANZONE, P., GUERRI, L., TACCARDI, B. and VIGANOTTI, C., 1985, Finite element approximation of regularized solutions of the inverse potential problem of electrocardiography and applications to experimental data, Calcolo, 22, 91–186
CRAVEN, P. and WAHBA G., 1979, Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross validation, Numer.Math., 31, 377–403
FOX, D. and PUCCI, C., 1958, The Dirichlet problem for the wave equation, Ann.Mat.Pura Appl. 46, 155–182
FRANKLIN, J.N., 1970, Well-posed stochastic extensions of ill-posed linear problems, J.Math. Anal.Appl. 31, 682–716
FRANKLIN, J.N., 1974, On Tikhonov's method for ill-posed problems, Math. Comp. 28, 889–907
GREGORY, R.T. and KARNEY, D.L., 1969, A Collection of Matrices for Testing Computational Algorithms (Wiley-Interscience, New York)
GREVILLE, T.N.E. (ed.), 1969, Theory and Applications of Spline Functions (Academic Press, New York)
GROETSCH, C.W., 1977, Generalized Inverses of Linear Operators (Dekker, New York)
GROETSCH, C.W., 1984, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Research Notes in Mathematics, Vol.105 (Pitman, Boston)
HADAMARD, J., 1923, Lectures on the Cauchy Problem in Linear Partial Differential Equations (Yale University Press, New Haven)
HERMAN, G.T., 1980, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography, (Academic Press, New York)
HILLE, E. and TAMARKIN, J.D., 1931, On the characteristic values of linear integral equations, Acta Math. 57, 1–76
HUANG, T.S., (ed.), 1975, Picture Processing and Digital Filtering, Topics in Applied Physics, Vol.6 (Springer, Berlin)
IVANOV, V.K., 1962, On linear problems which are not well-posed, Soviet Math.Dokl. 3, 981–983
IVANOV, V.K., 1966, The approximate solution of operator equations of the first kind, USSR Comp. Math. Math.Phys. 6, (No.6) 197–205
JOHN, F., 1955, Numerical solution of the equation of heat conduction for preceding times, Ann.Mat.Pura Appl. 40, 129–142
JOHN, F., 1960, Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math. 13, 551–585
KAMMERER, W.J. and NASHED, M.Z., 1971, Steepest descent for singular linear operators with nonclosed range, Applicable Analysis, 1, 143–159
KAMMERER, W.J. and NASHED, M.Z., 1972, On the convergence of the conjugate gradient method for singular linear operator equations, SIAM J.Numer.Anal., 9, 165–181
LANDWEBER, L., 1951, An iteration formula for Fredholm integral equations of the first kind, Amer.J.Math. 73, 615–624
LAVRENTIEV, M.M., 1967, Some Improperly Posed Problems of Mathematical Physics (Springer, Berlin)
LOUIS, A.K. and NATTERER, F., 1983, Mathematical problems of computerized tomography, Proc. IEEE, 71, 379–389
MILLER, K., 1964, Three circle theorems in partial differential equations and applications to improperly posed problems, Arch.Rat.Mech.Anal. 16, 126–154
MILLER, K., 1970, Least squares methods for ill-posed problems with a prescribed bound, SIAM J. Math.Anal. 1, 52–74
MOROZOV, V.A., 1968, The error principle in the solution of operational equations by the regularization method, USSR Comp.Math.Math.Phys. 8 (No.2), 63–87
MOROZOV, V.A., 1984, Methods for Solving Incorrectly Posed Problems (Springer, Berlin)
NASHED, M.Z. (ed.), 1976, Generalized Inverses and Applications (Academic Press, New York)
NASHED, M.Z., 1976, On moment-discretization and least-squares solutions of linear integral equations of the first kind, J.Math.Anal.Appl., 53, 359–366
PAPOULIS, A., 1968,,Systems and Transforms with Applications in Optics (McGraw-Hil, New York)
PAYNE, L.E., 1975, Improperly Posed Problems in Partial Differential Equations, Regional Conf.Series in Applied Math. (SIAM)
PHILLIPS, D.L., 1962, A technique for the numerical solution of certain integral equations of the first kind, J.Asso.Comput.Mach. 9, 84–97
PICARD, E., 1910, Sur un théorème géneral relatif aux equations integrales de première espèce et sur quelques problèmes de physique mathèmatique, R.C.Mat.Palermo, 29, 615–619
PUCCI, C., 1955, Sui problemi di Cauchy non "ben posti", Atti Acc.Naz.Lincei, 18, 473–477
REINSCH, C.H., 1967, Smoothing by spline functions, Numer.Math., 10, 177–183
ROBINSON, E.A., 1982, Spectral approach to geophysical inversion by Lorentz, Fourier and Radon transforms, Proc.IEEE, 70, 1039–1054
SABATIER, P.C. (ed.), 1978, Applied Inverse Problems, Lecture Notes in Physics, Vol.85 (Springer, Berlin)
SLEPIAN, D. and POLLAK, H.O., 1961, Prolate spheroidal wave functions, Fourier analysis and uncertainty — I, Bell System Tech. J. 40, 43–64
TALENTI, G., 1978, Sui problemi mal posti, Bollettino U.M.I. 15-A, 1–29
TIKHONOV, A.N., 1963, Solution of incorrectly formulated problems and the regularization method, Soviet Math.Dokl. 4, 1035–1038
TIKHONOV, A.N., 1963, Regularization of incorrectly posed problems, Soviet Math.Dokl. 4, 1624–1627
TIKHONOV, A.N. and ARSENIN, V.Y., 1977, Solutions of Ill-Posed Problems, translation ed. by F. John (Winston/Wiley, Washington)
TITCHMARSH, E.C., 1948, Introduction to the Theory of Fourier Integrals (Oxford University Press)
WAHBA, G., 1977, Practical approximate solutions to linear operator equations when the data are noisy, SIAM J.Numer.Anal., 14, 651–667
WESTWATER, E.R., SNIDER, J.B. and CARLSON, A.V., 1975, Experimental determination of temperature profiles by ground based microwave radiometry, J.Appl.Meteor., 14, 524–539
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Bertero, M. (1986). Regularization methods for linear inverse problems. In: Talenti, G. (eds) Inverse Problems. Lecture Notes in Mathematics, vol 1225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072660
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