Minimal-norm solution to the Fredholm integral equations of the first kind via the H-HK formulation
<|reference_start|>Minimal-norm solution to the Fredholm integral equations of the first kind via the H-HK formulation: The Fredholm integral equations of the first kind is a typical ill-posed problem, so that it is usually difficult to obtain its analytical minimal-norm solution. This paper gives a closed-form minimal-norm solution for the degenerate kernel equations based on the H-HK formulation. Furthermore, it has been shown that the structure of solutions to degenerate kernel equations and matrix equations are consistent. Subsequently, the obtained results are extended to non-degenerate integral equations. Finally, the validity and applicability of the proposed method are demonstrated by some examples.<|reference_end|>
@article{qiu2024minimal-norm,
    title={Minimal-norm solution to the Fredholm integral equations of the first
  kind via the H-HK formulation},
    author={Renjun Qiu and Ming Xu and Wei Qu},
    journal={arXiv preprint arXiv:2406.07303},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.07303},
    primaryClass={math.NA cs.NA}
}