The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
Solution of Sparse Indefinite Systems of Linear Equations
Abstract
The method of conjugate gradients for solving systems of linear equations with a symmetric positive definite matrix A is given as a logical development of the Lanczos algorithm for tridiagonalizing A. This approach suggests numerical algorithms for solving such systems when A is symmetric but indefinite. These methods have advantages when A is large and sparse.
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Cites
Methods of conjugate gradients for solving linear systems
Hestenes, M. R., & Stiefel, E. (1952) · Journal of Research of the National Bureau of Standards · doi:10.6028/jres.049.044 · Cited by 8,132
Lanczos, C. (1950) · Journal of Research of the National Bureau of Standards · doi:10.6028/jres.045.026 · Cited by 4,391
The Theory of Matrices in Numerical Analysis.
Haynsworth, E. V., & Householder, A. S. (1966) · The American Mathematical Monthly · doi:10.2307/2314680 · Cited by 1,363
Solution of systems of linear equations by minimized iterations
Lanczos, C. (1952) · Journal of Research of the National Bureau of Standards · doi:10.6028/jres.049.006 · Cited by 929
Least Squares Computations by Givens Transformations Without Square Roots
GENTLEMAN, W. M. (1973) · IMA Journal of Applied Mathematics · doi:10.1093/imamat/12.3.329 · Cited by 479
Computational Variants of the Lanczos Method for the Eigenproblem
PAIGE, C. C. (1972) · IMA Journal of Applied Mathematics · doi:10.1093/imamat/10.3.373 · Cited by 408
Self-citationA Note on Modifications to the Givens Plane Rotation
Hammarling, S. J. (1974) · IMA Journal of Applied Mathematics · doi:10.1093/imamat/13.2.215 · Cited by 118
Cited by
Eigenvalue computation in the 20th century
Golub, G. H., & van der Vorst, H. A. (2000) · Journal of Computational and Applied Mathematics · doi:10.1016/s0377-0427(00)00413-1 · Cited by 388
Recent computational developments in Krylov subspace methods for linear systems
Simoncini, V., & Szyld, D. B. (2007) · Numerical Linear Algebra with Applications · doi:10.1002/nla.499 · Cited by 375
Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application
Avdeev, D. B. (2005) · Surveys in Geophysics · doi:10.1007/s10712-005-1836-x · Cited by 276
PETSc/TAO Users Manual (Rev. 3.19)
Argonne National Laboratory (ANL), A., Balay, S., USDOE Office of Science (SC), A. S. C. R. (., Abhyankar, S., Adams, M., Benson, S., Brown, J., Brune, P., Buschelman, K., Constantinescu, E., et al. (2023) · doi:10.2172/1968587 · Cited by 67
Metadata
- Authors
- Paige, C. C., & Saunders, M. A.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1975-09
- Volume
- 12
- Issue
- 4
- Pages
- 617-629
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W2018850201
- Cited by
- 1,620
- References
- 7
- FWCI
- 5.28
- Type
- journal article
- Language
- en
- Open access
- closed
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- Paige, C. C., & Saunders, M. A. (1975). Solution of Sparse Indefinite Systems of Linear Equations. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0712047
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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