Any non-decreasing sequence of non-negative numbers can be the convergence curve of the DGMRES method

Q: How can I download an article?

To download an article from SID, first log in to the site, search for the article title, and click on the 'Download Article' option.

Q: How can I download an ISI article?

To download an ISI article on SID, enter the keyword or article title in the search bar, view the relevant results, click on the desired article, and select the 'Download Article' option.

Q: How can I access the SID database?

To access the SID database, visit SID.ir, create an account, and log in to access scientific resources.

Q: Is downloading articles from SID free?

Some articles on SID are available for free, while others require payment. Details are specified on the article's page.

Safarzadeh Malihe; Sadeghi Goughery Hossein

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2021 | Volume:7 | Issue:32 Page(s): 165-176

Download Full-Text

Persian Verion

View:

182

Download:

Cites:

Information Journal Paper

Title

Any non-decreasing sequence of non-negative numbers can be the convergence curve of the DGMRES method

Author(s)

Safarzadeh Malihe | Sadeghi Goughery Hossein | Issue Writer Certificate

Keywords

Singular linear system

index

Drazin

inverse

residual vector

Abstract

Investigating the convergence of the Krylov subspace methods has been considered as one of the favorite subjects in the field of numerical linear algebra. Given that the DGMRES method is a Krylov subspace methods, there is not much work to be done on its convergence. In this article we will discuss parts of the convergence of this method. We show that for any non-decreasing sequence of negative numbers f(0)≥ f(1)≥ ⋯ ≥ f(m-1)>f(m)=⋯ =f(n)=0, he set of {λ _1, … , λ _m, 0, … , 0} of the complex numbers and the arbitrary number α ≤ n-m can be a set of singular linear equations n×n, Ax=b with the index α and the set {λ _1, … , λ _m, 0, … , 0} as the spectrum of matrix A such that if the DGMRES method is used to solve this system, assuming ‖ A^α r_0 ‖ _2=f(0)‖ _2 = f (0), for k=1, … , m-1, the k^th residual vector is ‖ A^α 〖 r 〗 _k ‖ _2=f(k), wherer_0=b-Ax_0 is the initial residual vector. We attempt to do this by constructing the complete coefficient matrix of the system (s).

Cites

No record.

References

No record.

Cite

APA: Copy

Safarzadeh, Malihe, & Sadeghi Goughery, Hossein. (2021). Any non-decreasing sequence of non-negative numbers can be the convergence curve of the DGMRES method. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 7(32 ), 165-176. SID. https://sid.ir/paper/950645/en

Vancouver: Copy

Safarzadeh Malihe, Sadeghi Goughery Hossein. Any non-decreasing sequence of non-negative numbers can be the convergence curve of the DGMRES method. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2021;7(32 ):165-176. Available from: https://sid.ir/paper/950645/en

IEEE: Copy

Malihe Safarzadeh, and Hossein Sadeghi Goughery, “Any non-decreasing sequence of non-negative numbers can be the convergence curve of the DGMRES method,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 7, no. 32 , pp. 165–176, 2021, [Online]. Available: https://sid.ir/paper/950645/en

Related Journal Papers

No record.

Related Seminar Papers

No record.

Related Plans

No record.

Recommended Workshops