A new algorithm for solving ill-conditioned linear systems

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

A new algorithm is presented for solving ill-conditioned linear equations. This method is radically different from conventional methods. We improve the condition of the linear equation first and then solve the well-conditioned one. The approximate solution is modified to get the exact solution. Numerical simulations show that the proposed method is effective enough to be applied to the practical finite element problems. Mathematical soundness of the algorithm is also shown. Several implementation techniques are discussed. It can be used not only for solving ill-conditioned equations but also for inverse problems and many other areas.

Original languageEnglish
Pages (from-to)1373-1376
Number of pages4
JournalIEEE Transactions on Magnetics
Volume32
Issue number3 PART 2
DOIs
Publication statusPublished - 1996
Externally publishedYes

Fingerprint

linear equations
linear systems
Linear equations
Linear systems
Inverse problems
Computer simulation
simulation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Physics and Astronomy (miscellaneous)

Cite this

A new algorithm for solving ill-conditioned linear systems. / Kim, Hyong Joong.

In: IEEE Transactions on Magnetics, Vol. 32, No. 3 PART 2, 1996, p. 1373-1376.

Research output: Contribution to journalArticle

@article{75f43bf51eae4369b1165e7e9af6238a,
title = "A new algorithm for solving ill-conditioned linear systems",
abstract = "A new algorithm is presented for solving ill-conditioned linear equations. This method is radically different from conventional methods. We improve the condition of the linear equation first and then solve the well-conditioned one. The approximate solution is modified to get the exact solution. Numerical simulations show that the proposed method is effective enough to be applied to the practical finite element problems. Mathematical soundness of the algorithm is also shown. Several implementation techniques are discussed. It can be used not only for solving ill-conditioned equations but also for inverse problems and many other areas.",
author = "Kim, {Hyong Joong}",
year = "1996",
doi = "10.1109/20.497502",
language = "English",
volume = "32",
pages = "1373--1376",
journal = "IEEE Transactions on Magnetics",
issn = "0018-9464",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3 PART 2",

}

TY - JOUR

T1 - A new algorithm for solving ill-conditioned linear systems

AU - Kim, Hyong Joong

PY - 1996

Y1 - 1996

N2 - A new algorithm is presented for solving ill-conditioned linear equations. This method is radically different from conventional methods. We improve the condition of the linear equation first and then solve the well-conditioned one. The approximate solution is modified to get the exact solution. Numerical simulations show that the proposed method is effective enough to be applied to the practical finite element problems. Mathematical soundness of the algorithm is also shown. Several implementation techniques are discussed. It can be used not only for solving ill-conditioned equations but also for inverse problems and many other areas.

AB - A new algorithm is presented for solving ill-conditioned linear equations. This method is radically different from conventional methods. We improve the condition of the linear equation first and then solve the well-conditioned one. The approximate solution is modified to get the exact solution. Numerical simulations show that the proposed method is effective enough to be applied to the practical finite element problems. Mathematical soundness of the algorithm is also shown. Several implementation techniques are discussed. It can be used not only for solving ill-conditioned equations but also for inverse problems and many other areas.

UR - http://www.scopus.com/inward/record.url?scp=0030141909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030141909&partnerID=8YFLogxK

U2 - 10.1109/20.497502

DO - 10.1109/20.497502

M3 - Article

AN - SCOPUS:0030141909

VL - 32

SP - 1373

EP - 1376

JO - IEEE Transactions on Magnetics

JF - IEEE Transactions on Magnetics

SN - 0018-9464

IS - 3 PART 2

ER -