SCOPUS 정보 검색 플랫폼

Volumn 26, Issue 1, 1978, Pages 43-65

The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002497330 PISSN: 00219991 EISSN: 10902716 Source Type: Journal
DOI: 10.1016/0021-9991(78)90098-0 Document Type: Review

Times cited : (750)

References (14)

1
- 84966225158
- An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
- to appear
- (1977) Math. Comp. January
- Meuerink¹ Van Der Vorst²

2
- 84882127888
- Numerical Simulation of the High Density Approach to Laser Fusion
- Livermore, Ca.
- (1973) Lawrence Livermore Laboratory preprint, UCRL-74811
- Zimmerman¹

3
- 0000135303
- Methods of conjugate gradients for solving linear systems
- (1952) Journal of Research of the National Bureau of Standards , vol.49 , pp. 409-436
- Hestenes¹ Stiefel²

4
- 0002655630
- On the method of conjugate gradients for the solution of large sparse systems of linear equations
- Academic Press, New York
- (1971) Proceedings of the Conference on Large Sparse Systems of Linear Equations
- Reid¹

5
- 84916017092
- A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations
- Berkeley, Ca.
- (1975) Lawrence Berkeley Laboratory Pub. LBL-4604
- Concus¹ Golub² O'Leary³

6
- 17844403608
- Practical solution of linear equations and inversion of matrices
- (1954) Nat. Bur. Standards Appl. Math. Ser. , vol.39 , pp. 1-54
- Fox¹

8
- 0003660674
- Oxford Univ. Press, London, see Chapter 9, Section 2, for the power method and Chapter 6, Section 5, for a discussion of the Lanczos method
- (1965) The Algebraic Eigenvalue Problem
- Wilkinson¹

10
- 84916017089
- This problem is discussed by H. L. STONE, Iterative solution of implicit approximations of multidimensional partial differential equations, SIAM J. Numer. Anal. 5 (1968), 530–558, in Section 4 of his article. I have discussed Stone's method only for α = 0 because for problems of our generality (arbitrary variations in diffusion coefficient) there is no theoretical basis for choosing α and furthermore, his ad hoc formula (26) for a must be in error because the left-hand side is dimensionless while the right-hand side has dimensions of length squared. Anyone wishing to compare my results with SIP can try it on the model problem (prob. #4) with a's of his own choosing.

11
- 0002626016
- Linear Algebra
- Springer-Verlag, New York, Chapters II/8 and II/3 of the
- (1971) Handbook for Automatic Computation , vol.2
- Wilkinson¹ Reinsch²

12
- 84916017092
- A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations
- Berkeley, Ca.
- (1975) Lawrence Berkeley Laboratory Pub. LBL-4604 , pp. 12
- Concus¹ Golub² O'Leary³

13
- 84916017092
- A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations
- Berkeley, Ca.
- (1975) Lawrence Berkeley Laboratory Pub. LBL-4604 , pp. 13
- Concus¹ Golub² O'Leary³

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