A variational parameters-to-estimate-free nonlinear solver
S. Petrova, P.S. Vassilevski, in: L. Vulkov, J. Waśniewski, P. Yalamov (Eds.), Numerical Analysis and Its Applications, Springer Berlin Heidelberg, Berlin, Heidelberg, 1997, pp. 396–405.
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Konferenzbeitrag
| Veröffentlicht
| Englisch
Autor*in
Petrova, Svetozara
;
Vassilevski, Panayot S.
;
Vassilevski, Panayot S.Herausgeber*in
Vulkov, Lubin;
Waśniewski, Jerzy;
Yalamov, Plamen
Abstract
The paper introduces and analyzes an extension of the simple steepest descent variational iterative method for solving nonlinear equations defined from non-differentiable nonlinear mappings. This method is originally proposed for solving a class of nonlinear equations that arise in inner-outer iterative methods for solving linear equations with matrices of a two-by-two block form, see Axelsson and Vassilevski [2]. With minor modifications it turns out to be applicable to a more general class of nonlinear equations defined from non-differentiable mappings that are however sufficiently close to differentiable mappings in a neighborhood of the solution. An extension of the preconditioned steepest descent variational (PSD) method for solving semi-linear elliptic PDEs is illustrated with numerical experiments for a class of finite element discretization techniques based on two subspaces. The convergence of the PSD versus versions of Newton's method is compared and discussed.
Erscheinungsjahr
Titel des Konferenzbandes
Numerical Analysis and Its Applications
Seite
396-405
Konferenz
WNAA: International Workshop on Numerical Analysis and Its Applications
Konferenzort
Rousse, Bulgarien
Konferenzdatum
1996-06-24 – 1996-06-26
ISBN
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Petrova, Svetozara ; Vassilevski, Panayot S.: A variational parameters-to-estimate-free nonlinear solver. In: Vulkov, L. ; Waśniewski, J. ; Yalamov, P. (Hrsg.): Numerical Analysis and Its Applications, Lecture Notes in Computer Science. Berlin, Heidelberg : Springer Berlin Heidelberg, 1997, S. 396–405
Petrova S, Vassilevski PS. A variational parameters-to-estimate-free nonlinear solver. In: Vulkov L, Waśniewski J, Yalamov P, eds. Numerical Analysis and Its Applications. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg; 1997:396-405. doi:10.1007/3-540-62598-4_119
Petrova, S., & Vassilevski, P. S. (1997). A variational parameters-to-estimate-free nonlinear solver. In L. Vulkov, J. Waśniewski, & P. Yalamov (Eds.), Numerical Analysis and Its Applications (pp. 396–405). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-62598-4_119
@inproceedings{Petrova_Vassilevski_1997, place={Berlin, Heidelberg}, series={Lecture Notes in Computer Science}, title={A variational parameters-to-estimate-free nonlinear solver}, DOI={10.1007/3-540-62598-4_119}, booktitle={Numerical Analysis and Its Applications}, publisher={Springer Berlin Heidelberg}, author={Petrova, Svetozara and Vassilevski, Panayot S.}, editor={Vulkov, Lubin and Waśniewski, Jerzy and Yalamov, PlamenEditors}, year={1997}, pages={396–405}, collection={Lecture Notes in Computer Science} }
Petrova, Svetozara, and Panayot S. Vassilevski. “A Variational Parameters-to-Estimate-Free Nonlinear Solver.” In Numerical Analysis and Its Applications, edited by Lubin Vulkov, Jerzy Waśniewski, and Plamen Yalamov, 396–405. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. https://doi.org/10.1007/3-540-62598-4_119.
S. Petrova and P. S. Vassilevski, “A variational parameters-to-estimate-free nonlinear solver,” in Numerical Analysis and Its Applications, Rousse, Bulgarien, 1997, pp. 396–405.
Petrova, Svetozara, and Panayot S. Vassilevski. “A Variational Parameters-to-Estimate-Free Nonlinear Solver.” Numerical Analysis and Its Applications, edited by Lubin Vulkov et al., Springer Berlin Heidelberg, 1997, pp. 396–405, doi:10.1007/3-540-62598-4_119.
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