ΝΕΕΣ ΜΕΘΟΔΟΙ ΕΠΙΛΥΣΗΣ ΣΥΣΤΗΜΑΤΩΝ ΜΗ ΓΡΑΜΜΙΚΩΝ ΑΛΓΕΒΡΙΚΩΝ Η/ΚΑΙ ΥΠΕΡΒΑΤΙΚΩΝ ΕΞΙΣΩΣΕΩΝ

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.

Grantor dc:publisher

University of Patras

Year dc:date

1989

Authors dc:creator

• Γράψα-Αθανασίου, Θεοδούλα
• Grapsa, Theodoula

• 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

Language dc:language

gre

Identifier

10.12681/eadd/1259

OAI identifier oai:identifier

oai:10442/1259