Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Elements of Newtonian Mechanics Read chapter Read first chapter

2013 | OriginalPaper | Chapter

3. Solution of Systems of Linear Equations: Numerical Simulations

Authors : Luis Vázquez, Salvador Jiménez

Published in: Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems

Publisher: Springer New York

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

To check the usefulness of this method, we shall compare it with the simplest and well known iterative methods: Jacobi, Gauss-Seidel, and Steepest Descent [11, 14]. We shall do this through some examples but, first, let us recall how this other methods work.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Solution of Systems of Linear Equations
next chapter Eigenvalue Problems
Literature
1.
D.R. Anderson, D.J. Sweeney, T.A. Williams, Linear Programming for Decision Making (West Publishing, New York, 1974)
2.
P.M. Anselone, L.B. Rall, The solution of characteristic value-vector problems by Newton’s method. Numer. Math. 11, 38–45 (1968)MathSciNetCrossRefMATH
3.
M. Avriel, Nonlinear Programming. Analysis and Methods (Dover Publications, Mineola, 2003)
4.
E.M.L. Beale, Numerical Methods in Nonlinear Programming, ed. by J. Abadie (North Holland Publishing, Amsterdam, 1967)
5.
J.T. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, 2nd edn. SIAM’s Advances in Design and Control (2010)
6.
J.F. Bonnans, J.Ch. Gilbert, C. Lemarchal, C.A. Sagastizbal, Numerical Optimization: Theoretical and Practical Aspects (Springer, New York, 2006)MATH
7.
F. Chatelin, Eigenvalues of Matrices (Wiley, Chichester, 1995)
8.
K.A. Cliffe, T.J. Garratt, A. Spence, Eigenvalues of block matrices arising from problems in Fluid Mechanics. SIAM J. Matrix Anal. Appl. 15(4), 1310–1318 (1994).MathSciNetCrossRefMATH
9.
R. Cottle, E. Johnson, R. Wets, George B. Dantzig (1914–2005). Not. AMS 54(3), 344–369 (2007)
10.
G.B. Dantzig, Linear Programming and Extensions (Princeton University Press, Princeton, 1963)MATH
11.
V.N. Faddeeva, Computational Methods of Linear Algebra (Dover Publications, New York, 1959)MATH
12.
13.
H. Goldstein, Classical Mechanics (Addison-Wesley, Readings, 1981)
14.
G.H. Golub, Ch.F. Van Loan, Matrix Computations, 2nd edn. (Johns Hopkins, Baltimore, 1989)MATH
15.
J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vectors Fields (Springer, New York, 1983)
16.
E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration, 2nd edn. (Springer, New York, 2006)MATH
17.
18.
S. Jiménez, P. Pascual, C. Aguirre, L. Vázquez, A panoramic view of some perturbed nonlinear wave equations. Int. J. Bifurcat. Chaos 14(1), 1–40 (2004)CrossRefMATH
19.
S. Jiménez, L. Vázquez, A dynamics approach to the computation of eigenvectors of matrices. J. Comput. Math. 23(6), 657–672 (2005)MathSciNet
20.
21.
L.G. Khachiyan, A polynomial Algorithm in Linear Programming. Dokl. Akad. Nauk SSSR, 244(S), 1093–1096 (1979), translated in Soviet Mathematics Doklady 20(1), 191–194 (1979)
22.
V.V. Konotop, L. Vázquez, Nonlinear Random Waves (World Scientific, Singapore, 1994). See also references [379], [403], [326], [404] and [191], therein.
23.
M.C. Navarro, H. Herrero, A.M. Mancho, A. Wathen, Efficient solution of a generalized eigenvalue problem arising in a thermoconvective instability. Comm. Comput. Phys. 3(2), 308–329 (2008)MathSciNetMATH
24.
L. Perko, Differential Equations and Dynamical Systems, 3rd edn. (Springer, New York, 2001)MATH
25.
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, J.G.P. Barnes, Numerical Recipes in C. The Art of Scientific Computing, 2nd edn. (Cambridge University Press, Cambridge, 1995)
26.
M. Rossignoli, The Complete Pinball Book: Collecting the Game & Its History (Schiffer Publishing, Atglen, 2011)
27.
F. Santos, A counterexample to the Hirsch conjecture, arXiv:1006.2814 (2010)
28.
J. Stoer, R. Burslisch, Introduction to Numerical Analysis, 2nd edn. (Springer, New York, 2002)MATH
29.
30.
J. Todd, The condition number of the finite segment of the Hilbert matrix. Natl. Bur. Stand. Appl. Math. Ser. 39, 109–116 (1954)MathSciNet
31.
L. Vázquez, S. Jiménez, Analysis of a mechanical solver for linear systems of equations. J. Comput. Math. 19(1), 9–14 (2001)MathSciNetMATH
32.
L. Vázquez, J.L. Vázquez-Poletti, A new approach to solve systems of linear equations. J. Comput. Math. 19(4), 445–448 (2001)MathSciNetMATH
33.
Metadata
Title
Solution of Systems of Linear Equations: Numerical Simulations
Authors
Luis Vázquez
Salvador Jiménez
Copyright Year
2013
Publisher
Springer New York
Book
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems

Print ISBN: 978-1-4614-5911-8

Electronic ISBN: 978-1-4614-5912-5

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-5912-5_3

Premium Partners

    Image Credits