## Functiones et Approximatio Commentarii Mathematici

- Funct. Approx. Comment. Math.
- Volume 51, Number 1 (2014), 141-166.

### Expanding the applicability of a Two Step Newton-type projection method for ill-posed problems

Ioannis K. Argyros, Santhosh George, and Monnanda E. Shobha

#### Abstract

There are many classes of ill-posed problems that cannot be solved with existing iterative methods, since the usual Lipschitz-type assumptions are not satisfied. In this study, we expand the applicability of a two step Newton-type projection method considered in [10,11], using weaker assumptions. Numerical examples for the method and examples where the old assumptions are not satisfied but the new assumptions are satisfied are provided at the end of this study.

#### Article information

**Source**

Funct. Approx. Comment. Math., Volume 51, Number 1 (2014), 141-166.

**Dates**

First available in Project Euclid: 24 September 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.facm/1411564620

**Digital Object Identifier**

doi:10.7169/facm/2014.51.1.8

**Mathematical Reviews number (MathSciNet)**

MR3263074

**Zentralblatt MATH identifier**

1307.47071

**Subjects**

Primary: 47J06: Nonlinear ill-posed problems [See also 35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30] 65J15: Equations with nonlinear operators (do not use 65Hxx) 47H17

Secondary: 47A52: Ill-posed problems, regularization [See also 35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30] 65N20: Ill-posed problems 65J20: Improperly posed problems; regularization

**Keywords**

Discretized Two Step Newton Tikhonov method ill-posed Hammerstein-type operator equations balancing principle monotone operator regularization method projection method

#### Citation

Argyros, Ioannis K.; Shobha, Monnanda E.; George, Santhosh. Expanding the applicability of a Two Step Newton-type projection method for ill-posed problems. Funct. Approx. Comment. Math. 51 (2014), no. 1, 141--166. doi:10.7169/facm/2014.51.1.8. https://projecteuclid.org/euclid.facm/1411564620