References
- Gear CW. Differential algebraic equations, indices and integral algebraic equations. SIAM J Numer Anal. 1990;27:1527–1534.
- Wolfersdorf LV. On identification of memory kernel in linear theory of heat conduction. Math Methods Appl Sci. 1994;17:919–932.
- Janno J, Wolfersdorf LV. Inverse problems for identification of memory kernels in viscoelasticity. Fakultat fur Mathematik und Informatik, Technische Universitat Bergakademie Freiberg; 1996. (Technical Report 96-04).
- Jumarhon B, Lamb W, McKee S, et al. A Volterra integral type method for solving a class of nonlinear initial-boundary value problems. Numer Methods Partial Differ Equ. 1996;12:265–281.
- Liang H, Brunner H. Integral-algebraic equations: theory of collocation methods I. SIAM J Numer Anal. 2013;51(4):2238–2259.
- Lamm PK. Approximation of ill-posed Volterra problems via predictor-corrector regularization methods. SIAM J Appl Math. 1996;56(2):524–541.
- Kauthen JP. The numerical solution of Volterra integral-algebraic equations of index 1 by polynomial spline collocation method. Math Comp. 2000;70:1503–1514.
- Hadizadeh M, Ghoreishi F, Pishbin S. Jacobi spectral solution for integral-algebraic equations of index-2. Appl Numer Math. 2011;61:131–148.
- Pishbin S, Ghoreishi F, Hadizadeh M. A posteriori error estimation for the Legendre collocation method applied to integral-algebraic Volterra equations. Elect Trans Numer Anal. 2011;38:327–346.
- Pishbin S, Ghoreishi F, Hadizadeh M. The semi-explicit Volterra integral algebraic equations with weakly singular kernels: the numerical treatments. J Comput Appl Math. 2013;245:121–132.
- Budnikova OS, Bulatov MV. Numerical solution of integral-algebraic equations for multistep methods. Comput Math Math Phys. 2012;52(5):691–701.
- Liang H, Brunner H. Integral-algebraic equations: theory of collocation methods II. SIAM J Numer Anal. 2016;54(4):2640–2663.
- Brunner H. Collocation methods for Volterra integral and related functional equations. Cambridge: Cambridge University Press; 2004.
- Lamm PK. A survey of regularization methods for first-kind Volterra equations. In: Colton D, Engl HW, Louis HK, et al., editors. Surveys on solution methods for inverse problems. Vienna: Springer; 2000. p. 53–82.
- Plato R. Iterative and parametric methods for linear ill-posed problems. Habilitation thesis, TU Berlin, Berlin; 1995.
- Plato R. On the discrepancy principle for iterative and parametric methods to solve linear ill-posed equations. Numer Math. 1996;75(1):99–120.
- Morigi S, Reichel L, Sgallari F. An iterative Lavrentiev regularization method. BIT. 2006;46:589–606.
- George S, Pareth S. An application of Newton-type iterative method for the approximate implementation of Lavrentiev regularization. J Appl Anal. 2013;19(2):181–196.
- Pandolfi L. Adaptive recursive deconvolution and adaptive noise cancellation. Int J Control. 2007;80(3):403–415.
- Shubha VS, George S, Jidesh P. A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations. Numer Algorithms. 2015;68(2):289–304.
- Argyros I, George S, Kunhanandan M. Iterative regularization methods for ill-posed Hammerstein-type operator equations in Hilbert scales. Stud Univ Babes-Bolyai Math. 2014;59(2):247–262.
- Plato R. Lavrentiev’s method for linear Volterra integral equations of the first kind, with applications to the non-destructive testing of optical-fibre preforms. In: Rundell W, Engl HW, Louis AK, editors. Inverse problems in medical imaging and nondestructive testing (Oberwolfach, 1996). Vienna: Springer; 1997. p. 196–211.
- Plato R. The Galerkin scheme for Lavrentiev’s m-times iterated method to solve linear accretive Volterra integral equations of the first kind. BIT. 1997;37(2):404–423.
- Kittaneh F. Norm inequalities for sums of positive operators. J Operator Theory. 2002;48:95–103.
- Plato R. Converse results, saturation and quasi-optimality for Lavrentiev regularization of accretive problems. SIAM J Numer Anal. 2017;55(3):1315–1329.
- Hofmann B, Kaltenbacher B, Resmerita E. Lavrentiev’s regularization method in Hilbert spaces revisited. Inverse Prob Imaging. 2016;10:741–764.
- Bot R, Hofmann B. Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space. Inverse Prob. 2016;32:125003 (23pp).