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Conjugate gradient methods for indefinite systems

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Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 506))

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References

  1. Bunch, J.R., and Parlett, B.N., Direct methods for solving symetric indefinite systems of linear equations, S. I. A. M. J. Numer. Anal., Vol. 8, 1971, pp. 639–655.

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  2. Hestenes, M.R., and Stiefel, E., Methods of Conjugate Gradients for Solving Linear Systems, J. Res. Nat. Bur. Standards, Vol. 49, 1952, pp. 409–436.

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  3. Lanczos, C., An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators, J. Res. Nat. Bur. Standards, Vol. 45, 1950, pp. 255–282.

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  4. Lawson, C.L., Sparse Matrix Methods Based on Orthogonality and Conjugacy, Jet Propulsion Lab., Tech. Memo. 33–627, 1973.

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  5. Luenberger, D.G., Hyperbolic pairs in the method of conjugate gradients, S. I. A. M. J. Appl. Math., Vol. 17, 1969, pp. 1263–1267.

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  6. Paige, C.C., and Saunders, M.A., Solution of sparse indefinite systems of equations and least squares problems, Stanford University Report, STAN-CS-73-399, 1973.

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  7. Reid, J.K., On the Method of Conjugate Gradients for the Solution of Large Sparse Systems of Linear Equations, pp. 231–254 in Large Sparse Systems of Linear Equations, ed. J.K. Reid, Academic Press, London, 1971.

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  8. Rutishauser, H., Theory of gradient methods, Chapter 2 of Refined iterative methods for computation of the solution and the eigenvalues of self-adjoint boundary value problems, by M. Engeli, Th. Ginsburg, H. Rutishauser, and E. Stiefel, Birkhaüser, Basel, 1959.

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Authors
  1. R. Fletcher
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G. Alistair Watson

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© 1976 Springer-Verlag

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Fletcher, R. (1976). Conjugate gradient methods for indefinite systems. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080116

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  • DOI: https://doi.org/10.1007/BFb0080116

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07610-0

  • Online ISBN: 978-3-540-38129-7

  • eBook Packages: Springer Book Archive

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