Abstract
Most iterative methods for the solution of nonsymmetric linear systems of equations belong either to norm-reduction or projection methods. Two representatives of both classes, namely Euler methods for the first and Krylov methods for the second, are compared as convergence behaviour and computational effort are concerned.
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M. Eiermann, On the application of semiiterative methods generated by Faber polynomials to the solution of nonsymmetric linear equations. To appear in Numer. Math..
M. Eiermann, I. Marek and W. Niethammer, On the solution of singular linear systems of algebraic equations by semiiterative methods. To appear in Numer. Math..
M. Eiermann, W. Niethammer and R. S. Varga, A study of semiiterative methods for nonsymmetric systems of linear equations. Numer. Math. 47 (1985), 505–533.
M. Eierman, R. S. Varga and W. Niethammer, Iterationsverfahren für nichtsymmetrische Gleichungssysteme und Approximationsmethoden im Komplexen, Jber. d. Dt. Math.-Verein. 89 (1987), 1–32.
L. A. Hageman and D. M. Young, Applied Iterative Methods. New York -London — Toronto — Sydney — San Francisco, Academic Press 1981.
A. Householder, The Theory of Matrices in Numerical Analysis. New York — Toronto — London: Blaisdell Publ. Comp. 1964.
S. Kaczmarz, Angenäherte Auflösung von Systemen linearer Gleichungen. Bull. Intern. Acad. Polon. Sci. CLA (1937), 355–357.
F. Natterer, The Mathematics of Computerized Tomography. Stuttgart: Teubner 1986.
W. Niethammer and R. S. Varga, The analysis of k-step iterative methods for linear systems from summability theory. Numer. Math. 41 (1983), 177–206.
Y. Saad, Krylov subspace methods for solving large unsymmetric linear systems. Math. Comp. 37 (1981), 105–126.
Y. Saad, The Lanczos bi orthogonalization algorithm and other obligue projection methods for solving large unsymmetric systems. SIAM J. Numer. Anal. 19 (1982), 485–506.
Y. Saad and M. H. Schultz, Conjugate gradient-like algorithms for solving nonsymmetric linear systems. Math. Comp. 44 (1985), 417–424.
D. C. Smolarski and P. E. Saylor, An optimum iterative method for solving any linear system with a square matrix. BIT 28 (1988), 163–178.
U. Schulte, Krylov-Verfahren und semiiterative Verfahren zur Lösung nichtsymmetrischer linearer Gleichungssysteme. Diplomarbeit, Inst. f. Prakt. Math., Univ. Karlsruhe. Not published.
R. S. Varga, Matrix Iterative Analysis, Englewood Cliffs, NJ: Prentice Hall 1962.
D. M. Young, Iterative Solution of Large Linear Systems. New York: Academic Press 1971.
D. M. Young and K. C. Jea, Generalized conjugate gradient acceleration of iterative methods: Part II, the nonsymmetrziable case. Rep. CNA-163, Center of Numerical Analysis, University of Texas at Austin.
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Niethammer, W. (1988). Iterative Solution of Non-Symmetric Systems of Linear Equations. In: Agarwal, R.P., Chow, Y.M., Wilson, S.J. (eds) Numerical Mathematics Singapore 1988. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 86. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6303-2_31
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DOI: https://doi.org/10.1007/978-3-0348-6303-2_31
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