{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1259"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1259","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΝΕΕΣ ΜΕΘΟΔΟΙ ΕΠΙΛΥΣΗΣ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΑΛΓΕΒΡΙΚΩΝ Η/ΚΑΙ ΥΠΕΡΒΑΤΙΚΩΝ ΕΞΙΣΩΣΕΩΝ","abstract":"SOME NEW METHODS FOR SOLVING SYSTEMS OF NONLINEAR ALGEBRAIC AND/OR TRANSCEDENTAL EQUATIONS ARE DEVELOPED. THE FIRST METHOD DEALS WITH SYSTEMS OF NONLINEAR EQUATIONS IN IR2 AND IT IS BASED ON REDUCTION TO SIMPLER ONE-DIMENSIONAL NONLINEAREQUATION. IT GENERATES A SEQUENCE OF POINTS IN IR WHICH CONVERGES QUADRATICALLY TO ONE COMPONENT OF THE SOLUTION AND AFTERWARDS IT EVALUATES THE OTHER COMPONENT USING ONE SIMPLE COMPUTATION. IT DOES NOT REQUIRE A GOOD INITIAL GUESS OF THE SOLUTION AND IT DOES NOT DIRECTLY NEED FUNCTION EVALUATIONS. A PROOF OF CONVERGENCE IS ALSO GIVEN. NEXT, THE ABOVE METHOD IN GENERALIZED AND A NEW ONE IS DEVELOPED FOR THE NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS IN IRN. SUBSEQUENTLY, A PROCEDURE IS INTRODUCED WHICH ACCELERATES THE CONVERGENCE OF ITERATIVE METHODS FOR THE NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS IN IRN. THIS PROCEDURE WAS A ROTATING HYPERPLANE IN IRN+1, WHOSE ROTATION AXIS DEPENDS ON THE CURRENT APPROXIMATION OF N-1 COMPONENTS OF THE SOLUTION. FINALLY, NUMERICAL APPLICATION OF ALL THE ABOVE METHODS ARE PRESENTED AND THE RESULTS ARECOMPARED WITH NEWTON'S METHOD.","abstract_html":"SOME NEW METHODS FOR SOLVING SYSTEMS OF NONLINEAR ALGEBRAIC AND/OR TRANSCEDENTAL EQUATIONS ARE DEVELOPED. THE FIRST METHOD DEALS WITH SYSTEMS OF NONLINEAR EQUATIONS IN IR2 AND IT IS BASED ON REDUCTION TO SIMPLER ONE-DIMENSIONAL NONLINEAREQUATION. IT GENERATES A SEQUENCE OF POINTS IN IR WHICH CONVERGES QUADRATICALLY TO ONE COMPONENT OF THE SOLUTION AND AFTERWARDS IT EVALUATES THE OTHER COMPONENT USING ONE SIMPLE COMPUTATION. IT DOES NOT REQUIRE A GOOD INITIAL GUESS OF THE SOLUTION AND IT DOES NOT DIRECTLY NEED FUNCTION EVALUATIONS. A PROOF OF CONVERGENCE IS ALSO GIVEN. NEXT, THE ABOVE METHOD IN GENERALIZED AND A NEW ONE IS DEVELOPED FOR THE NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS IN IRN. SUBSEQUENTLY, A PROCEDURE IS INTRODUCED WHICH ACCELERATES THE CONVERGENCE OF ITERATIVE METHODS FOR THE NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS IN IRN. THIS PROCEDURE WAS A ROTATING HYPERPLANE IN IRN+1, WHOSE ROTATION AXIS DEPENDS ON THE CURRENT APPROXIMATION OF N-1 COMPONENTS OF THE SOLUTION. FINALLY, NUMERICAL APPLICATION OF ALL THE ABOVE METHODS ARE PRESENTED AND THE RESULTS ARECOMPARED WITH NEWTON'S METHOD.","abstract_has_math":false,"creators":["Γράψα-Αθανασίου, Θεοδούλα","Grapsa, Theodoula"],"institution":"University of Patras","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1989,"date_issued":"1989","date_published":"1989","updated_at":"2026-07-24T02:24:49Z","subjects":["ΑΡΙΘΜΗΤΙΚΗ ΛΥΣΗ","ΕΛΑΤΤΩΣΗ ΔΙΑΣΤΑΣΗΣ","ΘΕΩΡΗΜΑ ΠΕΠΛΕΓΜΕΝΩΝ ΣΥΝΑΡΤΗΣΕΩΝ","Μέθοδος Newton","ΜΕΘΟΔΟΣ SOR","ΜΕΘΟΔΟΣ ΔΙΧΟΤΟΜΗΣΗΣ","Μη γραμμικές εξισώσεις","Ρίζες","ΤΕΤΡΑΓΩΝΙΚΗ ΣΥΓΚΛΙΣΗ","BISECTION METHOD","DIMENSIONAL REDUCING","IMPLICIT FUNCTION THEOREM","Newton's method","NON LINEAR EQUATIONS","NUMERICAL SOLUTION","QUADRATIC CONVERGENCE","SOR METHOD","Zeros","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1259"],"render_values":[{"text":"10.12681/eadd/1259","href":"https://doi.org/10.12681/eadd/1259","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1259","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Γράψα-Αθανασίου, Θεοδούλα","Grapsa, Theodoula"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1989"]},{"key":"dc:publisher","label":"Institution","values":["University of Patras","Πανεπιστήμιο Πατρών"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ΑΡΙΘΜΗΤΙΚΗ ΛΥΣΗ","ΕΛΑΤΤΩΣΗ ΔΙΑΣΤΑΣΗΣ","ΘΕΩΡΗΜΑ ΠΕΠΛΕΓΜΕΝΩΝ ΣΥΝΑΡΤΗΣΕΩΝ","Μέθοδος Newton","ΜΕΘΟΔΟΣ SOR","ΜΕΘΟΔΟΣ ΔΙΧΟΤΟΜΗΣΗΣ","Μη γραμμικές εξισώσεις","Ρίζες","ΤΕΤΡΑΓΩΝΙΚΗ ΣΥΓΚΛΙΣΗ","BISECTION METHOD","DIMENSIONAL REDUCING","IMPLICIT FUNCTION THEOREM","Newton's method","NON LINEAR EQUATIONS","NUMERICAL SOLUTION","QUADRATIC CONVERGENCE","SOR METHOD","Zeros","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1259","http://hdl.handle.net/10442/hedi/1259"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["SOME NEW METHODS FOR SOLVING SYSTEMS OF NONLINEAR ALGEBRAIC AND/OR TRANSCEDENTAL EQUATIONS ARE DEVELOPED. THE FIRST METHOD DEALS WITH SYSTEMS OF NONLINEAR EQUATIONS IN IR2 AND IT IS BASED ON REDUCTION TO SIMPLER ONE-DIMENSIONAL NONLINEAREQUATION. IT GENERATES A SEQUENCE OF POINTS IN IR WHICH CONVERGES QUADRATICALLY TO ONE COMPONENT OF THE SOLUTION AND AFTERWARDS IT EVALUATES THE OTHER COMPONENT USING ONE SIMPLE COMPUTATION. IT DOES NOT REQUIRE A GOOD INITIAL GUESS OF THE SOLUTION AND IT DOES NOT DIRECTLY NEED FUNCTION EVALUATIONS. A PROOF OF CONVERGENCE IS ALSO GIVEN. NEXT, THE ABOVE METHOD IN GENERALIZED AND A NEW ONE IS DEVELOPED FOR THE NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS IN IRN. SUBSEQUENTLY, A PROCEDURE IS INTRODUCED WHICH ACCELERATES THE CONVERGENCE OF ITERATIVE METHODS FOR THE NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS IN IRN. THIS PROCEDURE WAS A ROTATING HYPERPLANE IN IRN+1, WHOSE ROTATION AXIS DEPENDS ON THE CURRENT APPROXIMATION OF N-1 COMPONENTS OF THE SOLUTION. FINALLY, NUMERICAL APPLICATION OF ALL THE ABOVE METHODS ARE PRESENTED AND THE RESULTS ARECOMPARED WITH NEWTON'S METHOD.","ΑΝΑΠΤΥΞΗ ΝΕΩΝ ΜΕΘΟΔΩΝ ΓΙΑ ΤΗΝ ΑΡΙΘΜΗΤΙΚΗ ΕΠΙΛΥΣΗ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΑΛΓΕΒΡΙΚΩΝ 'Η/ΚΑΙ ΥΠΕΡΒΑΤΙΚΩΝ ΕΞΙΣΩΣΕΩΝ. Η ΠΡΩΤΗ ΜΕΘΟΔΟΣ ΑΝΑΦΕΡΕΤΑΙ ΣΕ ΣΥΣΤΗΜΑΤΑ ΜΗ ΓΡΑΜΜΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΣΤΟ IR2 ΚΑΙ ΒΑΣΙΖΕΤΑΙ ΣΤΗΝ ΑΝΑΓΩΓΗ ΤΟΥΣ ΣΕ ΑΠΛΟΥΣΤΕΡΕΣ ΜΟΝΟΔΙΑΣΤΑΤΕΣ ΜΗ ΓΡΑΜΜΙΚΕΣ ΕΞΙΣΩΣΕΙΣ. ΑΥΤΗ Η ΜΕΘΟΔΟΣ ΔΗΜΙΟΥΡΓΕΙ ΜΙΑ ΑΚΟΛΟΥΘΙΑ ΣΗΜΕΙΩΝ ΣΤΟΝ IR ΠΟΥ ΣΥΓΚΛΙΝΕΙ ΤΕΤΡΑΓΩΝΙΚΑ ΣΤΗΝ ΜΙΑ ΣΥΝΙΣΤΩΣΑ ΤΗΣ ΛΥΣΗΣ ΚΑΙ ΜΕΤΑ, ΜΕ ΕΝΑΝ ΑΠΛΟ ΥΠΟΛΟΓΙΣΜΟ ΒΡΙΣΚΕΙ ΤΗΝ ΑΛΛΗ ΣΥΝΙΣΤΩΣΑ. ΔΕΝ ΧΡΕΙΑΖΕΤΑΙ ΚΑΛΗ ΑΡΧΙΚΗ ΠΡΟΣΕΓΓΙΣΗ ΓΙΑ ΤΗΝ ΜΙΑ ΣΥΝΤΕΤΑΓΜΕΝΗ ΤΗΣ ΛΥΣΗΣ ΚΑΙ ΔΕΝ ΑΠΟΚΤΟΥΝΤΑΙ ΑΠ' ΕΥΘΕΙΑΣ ΣΥΝΑΡΤΗΣΙΑΚΟΙ ΥΠΟΛΟΓΙΣΜΟΙ. ΔΙΝΕΤΑΙ ΑΠΟΔΕΙΞΗ ΤΗΣ ΣΥΓΚΛΙΣΗΣ ΤΗΣ ΜΕΘΟΔΟΥ. ΣΤΗΝ ΣΥΝΕΧΕΙΑΗ ΠΑΡΑΠΑΝΩ ΜΕΘΟΔΟΣ ΓΕΝΙΚΕΥΕΤΑΙ ΓΙΑ ΤΗΝ ΠΕΡΙΠΤΩΣΗ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΣΤΟΝ IRN. ΠΑΡΟΥΣΙΑΣΗ ΜΙΑΣ ΝΕΑΣ ΜΕΘΟΔΟΥ ΠΟΥ ΕΠΙΤΑΧΥΝΕΙ ΤΗΝ ΣΥΓΚΛΙΣΗ ΤΩΝ ΕΠΑΝΑΛΗΠΤΙΚΩΝ ΜΕΘΟΔΩΝ ΑΡΙΘΜΗΤΙΚΗΣ ΕΠΙΛΥΣΗΣ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΣΤΟΝ IRN. Η ΔΙΑΔΙΚΑΣΙΑ ΑΥΤΗ ΒΑΣΙΖΕΤΑΙ ΣΤΗΝ ΠΕΡΙΣΤΡΟΦΗ ΕΝΟΣ ΥΠΕΡΕΠΙΠΕΔΟΥ ΣΤΟΝ IRN. Η ΔΙΑΔΙΚΑΣΙΑ ΑΥΤΗ ΒΑΣΙΖΕΤΑΙ ΣΤΗΝ ΠΕΡΙΣΤΡΟΦΗ ΕΝΟΣ ΥΠΕΡΕΠΙΠΕΔΟΥ ΣΤΟΝ IRN+1, ΤΟΥ ΟΠΟΙΟΥ Ο ΑΞΟΝΑΣ ΠΕΡΙΣΤΡΟΦΗΣ ΕΞΑΡΤΑΤΑΙ ΑΠΟ ΤΗΝ ΤΡΕΧΟΥΣΑ ΠΡΟΣΕΓΓΙΣΗ ΤΩΝ Ν-1 ΣΥΝΙΣΤΩΣΩΝ ΤΗΣ ΛΥΣΗΣ. ΠΑΡΑΘΕΣΗ ΑΡΙΘΜΗΤΙΚΩΝ ΕΦΑΡΜΟΓΩΝ ΟΛΩΝ ΤΩΝ ΠΑΡΑΠΑΝΩ ΝΕΩΝ ΜΕΘΟΔΩΝ, ΚΑΙ ΣΥΓΚΡΙΣΗ ΤΩΝ ΑΠΟΤΕΛΕΣΜΑΤΩΝ ΤΟΥΣ ΜΕ ΤΑ ΑΝΤΙΣΤΟΙΧΑ ΤΗΣ ΜΕΘΟΔΟΥ NEWTON."]},{"key":"dc:title","label":"Title","values":["ΝΕΕΣ ΜΕΘΟΔΟΙ ΕΠΙΛΥΣΗΣ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΑΛΓΕΒΡΙΚΩΝ Η/ΚΑΙ ΥΠΕΡΒΑΤΙΚΩΝ ΕΞΙΣΩΣΕΩΝ","NEW METHODS FOR SOLVING SYSTEMS OF NONLINEAR ALGEBRAIC AND/OR TRANSCENDENTAL EQUATIONS"]}]}],"canonical_facts":{"dc:creator":["Γράψα-Αθανασίου, Θεοδούλα","Grapsa, Theodoula"],"dc:date":["1989"],"dc:description":["SOME NEW METHODS FOR SOLVING SYSTEMS OF NONLINEAR ALGEBRAIC AND/OR TRANSCEDENTAL EQUATIONS ARE DEVELOPED. THE FIRST METHOD DEALS WITH SYSTEMS OF NONLINEAR EQUATIONS IN IR2 AND IT IS BASED ON REDUCTION TO SIMPLER ONE-DIMENSIONAL NONLINEAREQUATION. IT GENERATES A SEQUENCE OF POINTS IN IR WHICH CONVERGES QUADRATICALLY TO ONE COMPONENT OF THE SOLUTION AND AFTERWARDS IT EVALUATES THE OTHER COMPONENT USING ONE SIMPLE COMPUTATION. IT DOES NOT REQUIRE A GOOD INITIAL GUESS OF THE SOLUTION AND IT DOES NOT DIRECTLY NEED FUNCTION EVALUATIONS. A PROOF OF CONVERGENCE IS ALSO GIVEN. NEXT, THE ABOVE METHOD IN GENERALIZED AND A NEW ONE IS DEVELOPED FOR THE NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS IN IRN. SUBSEQUENTLY, A PROCEDURE IS INTRODUCED WHICH ACCELERATES THE CONVERGENCE OF ITERATIVE METHODS FOR THE NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS IN IRN. THIS PROCEDURE WAS A ROTATING HYPERPLANE IN IRN+1, WHOSE ROTATION AXIS DEPENDS ON THE CURRENT APPROXIMATION OF N-1 COMPONENTS OF THE SOLUTION. FINALLY, NUMERICAL APPLICATION OF ALL THE ABOVE METHODS ARE PRESENTED AND THE RESULTS ARECOMPARED WITH NEWTON'S METHOD.","ΑΝΑΠΤΥΞΗ ΝΕΩΝ ΜΕΘΟΔΩΝ ΓΙΑ ΤΗΝ ΑΡΙΘΜΗΤΙΚΗ ΕΠΙΛΥΣΗ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΑΛΓΕΒΡΙΚΩΝ 'Η/ΚΑΙ ΥΠΕΡΒΑΤΙΚΩΝ ΕΞΙΣΩΣΕΩΝ. Η ΠΡΩΤΗ ΜΕΘΟΔΟΣ ΑΝΑΦΕΡΕΤΑΙ ΣΕ ΣΥΣΤΗΜΑΤΑ ΜΗ ΓΡΑΜΜΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΣΤΟ IR2 ΚΑΙ ΒΑΣΙΖΕΤΑΙ ΣΤΗΝ ΑΝΑΓΩΓΗ ΤΟΥΣ ΣΕ ΑΠΛΟΥΣΤΕΡΕΣ ΜΟΝΟΔΙΑΣΤΑΤΕΣ ΜΗ ΓΡΑΜΜΙΚΕΣ ΕΞΙΣΩΣΕΙΣ. ΑΥΤΗ Η ΜΕΘΟΔΟΣ ΔΗΜΙΟΥΡΓΕΙ ΜΙΑ ΑΚΟΛΟΥΘΙΑ ΣΗΜΕΙΩΝ ΣΤΟΝ IR ΠΟΥ ΣΥΓΚΛΙΝΕΙ ΤΕΤΡΑΓΩΝΙΚΑ ΣΤΗΝ ΜΙΑ ΣΥΝΙΣΤΩΣΑ ΤΗΣ ΛΥΣΗΣ ΚΑΙ ΜΕΤΑ, ΜΕ ΕΝΑΝ ΑΠΛΟ ΥΠΟΛΟΓΙΣΜΟ ΒΡΙΣΚΕΙ ΤΗΝ ΑΛΛΗ ΣΥΝΙΣΤΩΣΑ. ΔΕΝ ΧΡΕΙΑΖΕΤΑΙ ΚΑΛΗ ΑΡΧΙΚΗ ΠΡΟΣΕΓΓΙΣΗ ΓΙΑ ΤΗΝ ΜΙΑ ΣΥΝΤΕΤΑΓΜΕΝΗ ΤΗΣ ΛΥΣΗΣ ΚΑΙ ΔΕΝ ΑΠΟΚΤΟΥΝΤΑΙ ΑΠ' ΕΥΘΕΙΑΣ ΣΥΝΑΡΤΗΣΙΑΚΟΙ ΥΠΟΛΟΓΙΣΜΟΙ. ΔΙΝΕΤΑΙ ΑΠΟΔΕΙΞΗ ΤΗΣ ΣΥΓΚΛΙΣΗΣ ΤΗΣ ΜΕΘΟΔΟΥ. ΣΤΗΝ ΣΥΝΕΧΕΙΑΗ ΠΑΡΑΠΑΝΩ ΜΕΘΟΔΟΣ ΓΕΝΙΚΕΥΕΤΑΙ ΓΙΑ ΤΗΝ ΠΕΡΙΠΤΩΣΗ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΣΤΟΝ IRN. ΠΑΡΟΥΣΙΑΣΗ ΜΙΑΣ ΝΕΑΣ ΜΕΘΟΔΟΥ ΠΟΥ ΕΠΙΤΑΧΥΝΕΙ ΤΗΝ ΣΥΓΚΛΙΣΗ ΤΩΝ ΕΠΑΝΑΛΗΠΤΙΚΩΝ ΜΕΘΟΔΩΝ ΑΡΙΘΜΗΤΙΚΗΣ ΕΠΙΛΥΣΗΣ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΣΤΟΝ IRN. Η ΔΙΑΔΙΚΑΣΙΑ ΑΥΤΗ ΒΑΣΙΖΕΤΑΙ ΣΤΗΝ ΠΕΡΙΣΤΡΟΦΗ ΕΝΟΣ ΥΠΕΡΕΠΙΠΕΔΟΥ ΣΤΟΝ IRN. Η ΔΙΑΔΙΚΑΣΙΑ ΑΥΤΗ ΒΑΣΙΖΕΤΑΙ ΣΤΗΝ ΠΕΡΙΣΤΡΟΦΗ ΕΝΟΣ ΥΠΕΡΕΠΙΠΕΔΟΥ ΣΤΟΝ IRN+1, ΤΟΥ ΟΠΟΙΟΥ Ο ΑΞΟΝΑΣ ΠΕΡΙΣΤΡΟΦΗΣ ΕΞΑΡΤΑΤΑΙ ΑΠΟ ΤΗΝ ΤΡΕΧΟΥΣΑ ΠΡΟΣΕΓΓΙΣΗ ΤΩΝ Ν-1 ΣΥΝΙΣΤΩΣΩΝ ΤΗΣ ΛΥΣΗΣ. ΠΑΡΑΘΕΣΗ ΑΡΙΘΜΗΤΙΚΩΝ ΕΦΑΡΜΟΓΩΝ ΟΛΩΝ ΤΩΝ ΠΑΡΑΠΑΝΩ ΝΕΩΝ ΜΕΘΟΔΩΝ, ΚΑΙ ΣΥΓΚΡΙΣΗ ΤΩΝ ΑΠΟΤΕΛΕΣΜΑΤΩΝ ΤΟΥΣ ΜΕ ΤΑ ΑΝΤΙΣΤΟΙΧΑ ΤΗΣ ΜΕΘΟΔΟΥ NEWTON."],"dc:identifier":["10.12681/eadd/1259","http://hdl.handle.net/10442/hedi/1259"],"dc:language":["gre"],"dc:publisher":["University of Patras","Πανεπιστήμιο Πατρών"],"dc:subject":["ΑΡΙΘΜΗΤΙΚΗ ΛΥΣΗ","ΕΛΑΤΤΩΣΗ ΔΙΑΣΤΑΣΗΣ","ΘΕΩΡΗΜΑ ΠΕΠΛΕΓΜΕΝΩΝ ΣΥΝΑΡΤΗΣΕΩΝ","Μέθοδος Newton","ΜΕΘΟΔΟΣ SOR","ΜΕΘΟΔΟΣ ΔΙΧΟΤΟΜΗΣΗΣ","Μη γραμμικές εξισώσεις","Ρίζες","ΤΕΤΡΑΓΩΝΙΚΗ ΣΥΓΚΛΙΣΗ","BISECTION METHOD","DIMENSIONAL REDUCING","IMPLICIT FUNCTION THEOREM","Newton's method","NON LINEAR EQUATIONS","NUMERICAL SOLUTION","QUADRATIC CONVERGENCE","SOR METHOD","Zeros","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"dc:title":["ΝΕΕΣ ΜΕΘΟΔΟΙ ΕΠΙΛΥΣΗΣ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΑΛΓΕΒΡΙΚΩΝ Η/ΚΑΙ ΥΠΕΡΒΑΤΙΚΩΝ ΕΞΙΣΩΣΕΩΝ","NEW METHODS FOR SOLVING SYSTEMS OF NONLINEAR ALGEBRAIC AND/OR TRANSCENDENTAL EQUATIONS"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:49Z"}