Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear system of equations

Behnejad, Shiva and Khojasteh Salkuyeh, Davod (2010) Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear system of equations. Other thesis, University of Mohaghegh Ardabili.

[img] Text
92.pdf

Download (931kB)
Official URL: http://uma.ac.ir/

Abstract

Solving many problems in science and engineering leads to solve the linear system of equations Ax=b where the matrix A is large, sparse, non-Hermitian positive definite matrix and x,b∈C^n. As we know the Hermitian and skew-Hermitian (HSS) iterative method and its inexact version (IHSS) are quite suitable for these kind of systems. Li et al. in 2007 presented the lopsided HSS (LHSS) and its inexact version ILHSS. In this dissertation, the LHSS and ILHSS methods are investigated with complete details, including convergence of the method, choosing the used parameters and comparing with HSS and IHSS, respectively. Finally, we give several numerical examples to verify the convergence of these methods and comparing with the HSS and IHSS methods.

Item Type: Thesis (Other)
Persian Title: روش هاي شكافت هرميتي – هرميتي كج اصلاح شده براي حل دســتگاه معادلات خطي معين مثبت غيرهرميتي
Persian Abstract: بسياري از مسائل در علوم و مهندسي منجر به حل دستگاه معادلات خطي Ax=bمي شوند كه در آن A يك ماتريس تنك معين مثبت غيرهرميتي با ابعاد بزرگ است و x,b∈C^n. همانطور كه مي دانيم روش هاي تكراري شكافت هرميتي و هرميتي كج (HSS) و نسخه ي تقريبي آن (IHSS) براي حل اين گونه دستگاه ها بسيار مناسب هستند. لي و همكارانش در سال 2007 روش هاي تکراری HSSيك طرفه (LHSS) و نسخه ی تقريبي آن (ILHSS) را ارائه نمودند. در اين پايان نامه روش های LHSS و ILHSS را با جزئيات كامل، از جمله همگرايي روش ها و انتخاب پارامترهاي مورد استفاده، بررسي كرده و به ترتيب با روش هاي HSS و IHSS مقايسه مي كنيم . در پايان چندين مثال عددي براي بررسي همگرايي اين روش ها و مقايسه با روش هاي HSS و IHSS ارائه مي كنيم .
Supervisor:
SupervisorE-mail
Khojasteh Salkuyeh, DavodUNSPECIFIED
Advisor:
AdvisorE-mail
-, -UNSPECIFIED
Subjects: Faculty of Basic Sciences > Department of Mathematics
Divisions > Faculty of Basic Sciences > Department of Mathematics
Divisions: Subjects > Faculty of Basic Sciences > Department of Mathematics
Faculty of Basic Sciences > Department of Mathematics
Date Deposited: 13 Jul 2019 07:13
Last Modified: 13 Jul 2019 07:13
URI: http://repository.uma.ac.ir/id/eprint/7770

Actions (login required)

View Item View Item