Infinite Linear Equations

P. N. Shivakumar, K. C. Sivakumar and Yang Zhang
Additional contact information
P. N. Shivakumar: University of Manitoba, Department of Mathematics
K. C. Sivakumar: Indian Institute of Technology, Madras, Department of Mathematics
Yang Zhang: University of Manitoba, Department of Mathematics

Chapter Chapter 3 in Infinite Matrices and Their Recent Applications, 2016, pp 27-39 from Springer

Abstract: Abstract In this chapter, we shall first review, in Sect. 3.2, certain results on infinite linear systems whose “coefficient” matrices are diagonally dominant in some sense. We treat these infinite matrices in their own right and also as operators over certain normed linear spaces. These results show the extent to which results that are known for finite matrices have been generalized. Next, in Sect. 3.3, we recall some results on eigenvalues for operators mainly of the type considered in the second section. We also review a powerful numerical method for computing eigenvalues of certain diagonally dominant tridiagonal operators. Section 3.4 concerns linear differential systems whose coefficient matrices are operators on either ℓ 1 or ℓ ∞ $$\ell^{\infty }$$ . Convergence results for truncated systems are presented. The concluding section, viz., Sect. 3.5 discusses an iterative method for numerically solving a linear equation whose matrix is treated as an operator on ℓ ∞ $$\ell^{\infty }$$ satisfying certain conditions, including a diagonal dominance condition.

Keywords: Infinite Linear System; Truncated System; Diagonal Dominance Condition; Powerful Numerical Methods; Normed Linear Space (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30180-8_3

Ordering information: This item can be ordered from
http://www.springer.com/9783319301808

DOI: 10.1007/978-3-319-30180-8_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().