Abstract. In this paper, we present an enhanced spectral correction for the DMDY conjugate gradient method. Our approach involves integrating a third term and determining its parameter through three different approaches. The primary objective is to ensure the sufficient descent condition. By applying the Wolfe line search conditions, we establish the global convergence property for all three proposed algorithms. Numerical tests conclusively demonstrate the superior efficiency of our algorithms, surpassing that of existing methods.

MSC: 90C06, 90C30, 65K05

Keywords: Spectral correction, Conjugate gradient methods, Sufficient descent condition and global convergence, Numerical tests.

DOI 10.56082/annalsarscimath.2024.1.24

Abstract Article Volume 16 no 1 / 2024

*Accepted for publication on January, 5-th, 2023

[1] khaoulameansri@gmail.com, k.meansri@univ-soukahras.dz Laboratory Informatics and Mathematics (LIM), University of Mohamed Cherif Messaadia Souk Ahras, B.P.1553, Souk Ahras, 41000, Algeria; Paper written with financial support of: Not supported

[2] noureddinebenrabia@yahoo.fr University of Mohamed Cherif Messaadia Souk Ahras, B.P.1553, Souk Ahras, 41000, Algeria, Laboratory of Applied Mathematics and Modeling

[3] mourad.ghi24@gmail.com, ghiat.mourad@univ-guelma.dz Laboratory of Applied Mathematics and Modeling, University of 8 Mai 1945 Guelma, B.P.401, Guelma, 24000, Algeria

[4] guebaihamza@yahoo.fr, guebbai.hamza@univ-guelma.dz Laboratory of Applied Mathematics and Modeling, University of 8 Mai 1945 Guelma, B.P.401, Guelma, 24000, Algeria

[5] hafaidia.imane@yahoo.com Constantine 1 - Freres Mentouri University, Laboratory of Applied Mathematics and Modeling, University of 8 Mai 1945 Guelma, B.P.401, Guelma, 24000, Algeria