{"publication_identifier":{"isbn":["978-3-540-62598-8"],"issn":["0302-9743"],"eissn":["1611-3349"],"eisbn":["978-3-540-68326-1"]},"publication":"Numerical Analysis and Its Applications","date_updated":"2024-07-17T09:55:42Z","extern":"1","date_created":"2024-05-29T08:24:14Z","user_id":"220548","editor":[{"first_name":"Lubin","full_name":"Vulkov, Lubin","last_name":"Vulkov"},{"last_name":"Waśniewski","full_name":"Waśniewski, Jerzy","first_name":"Jerzy"},{"first_name":"Plamen","last_name":"Yalamov","full_name":"Yalamov, Plamen"}],"page":"396-405","conference":{"end_date":"1996-06-26","start_date":"1996-06-24","name":"WNAA: International Workshop on Numerical Analysis and Its Applications","location":"Rousse, Bulgarien"},"author":[{"id":"201871","first_name":"Svetozara","full_name":"Petrova, Svetozara","last_name":"Petrova"},{"first_name":"Panayot S.","full_name":"Vassilevski, Panayot S.","last_name":"Vassilevski"}],"publisher":"Springer Berlin Heidelberg","doi":"10.1007/3-540-62598-4_119","project":[{"_id":"f432a2ee-bceb-11ed-a251-a83585c5074d","name":"Institute for Data Science Solutions"}],"status":"public","_id":"4606","place":"Berlin, Heidelberg","title":"A variational parameters-to-estimate-free nonlinear solver","type":"conference","year":"1997","publication_status":"published","citation":{"alphadin":"<span style=\"font-variant:small-caps;\">Petrova, Svetozara</span> ; <span style=\"font-variant:small-caps;\">Vassilevski, Panayot S.</span>: A variational parameters-to-estimate-free nonlinear solver. In: <span style=\"font-variant:small-caps;\">Vulkov, L.</span> ; <span style=\"font-variant:small-caps;\">Waśniewski, J.</span> ; <span style=\"font-variant:small-caps;\">Yalamov, P.</span> (Hrsg.): <i>Numerical Analysis and Its Applications</i>, <i>Lecture Notes in Computer Science</i>. Berlin, Heidelberg : Springer Berlin Heidelberg, 1997, S. 396–405","chicago":"Petrova, Svetozara, and Panayot S. Vassilevski. “A Variational Parameters-to-Estimate-Free Nonlinear Solver.” In <i>Numerical Analysis and Its Applications</i>, edited by Lubin Vulkov, Jerzy Waśniewski, and Plamen Yalamov, 396–405. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. <a href=\"https://doi.org/10.1007/3-540-62598-4_119\">https://doi.org/10.1007/3-540-62598-4_119</a>.","bibtex":"@inproceedings{Petrova_Vassilevski_1997, place={Berlin, Heidelberg}, series={Lecture Notes in Computer Science}, title={A variational parameters-to-estimate-free nonlinear solver}, DOI={<a href=\"https://doi.org/10.1007/3-540-62598-4_119\">10.1007/3-540-62598-4_119</a>}, 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} }","mla":"Petrova, Svetozara, and Panayot S. Vassilevski. “A Variational Parameters-to-Estimate-Free Nonlinear Solver.” <i>Numerical Analysis and Its Applications</i>, edited by Lubin Vulkov et al., Springer Berlin Heidelberg, 1997, pp. 396–405, doi:<a href=\"https://doi.org/10.1007/3-540-62598-4_119\">10.1007/3-540-62598-4_119</a>.","short":"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.","ama":"Petrova S, Vassilevski PS. A variational parameters-to-estimate-free nonlinear solver. In: Vulkov L, Waśniewski J, Yalamov P, eds. <i>Numerical Analysis and Its Applications</i>. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg; 1997:396-405. doi:<a href=\"https://doi.org/10.1007/3-540-62598-4_119\">10.1007/3-540-62598-4_119</a>","apa":"Petrova, S., &#38; Vassilevski, P. S. (1997). A variational parameters-to-estimate-free nonlinear solver. In L. Vulkov, J. Waśniewski, &#38; P. Yalamov (Eds.), <i>Numerical Analysis and Its Applications</i> (pp. 396–405). Berlin, Heidelberg: Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/3-540-62598-4_119\">https://doi.org/10.1007/3-540-62598-4_119</a>","ieee":"S. Petrova and P. S. Vassilevski, “A variational parameters-to-estimate-free nonlinear solver,” in <i>Numerical Analysis and Its Applications</i>, Rousse, Bulgarien, 1997, pp. 396–405."},"series_title":"Lecture Notes in Computer Science","alternative_id":["4769"],"abstract":[{"lang":"eng","text":"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."}],"language":[{"iso":"eng"}]}