Methods of Conjugate Gradients for Solving Linear Systems

Hestenes, M. R., & Stiefel, E. (1952). Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau of Standards, 49(6), 409-436.

Type

Journal article

Intellectual base

Primary research

Year

1952

DOI

10.6028/jres.049.044

Link

https://nvlpubs.nist.gov/nistpubs/jres/049/jresv49n6p409_A1b.pdf

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Conjugate Gradient Method
  • Starting from \(x_0\), CG builds iterates in expanding Krylov subspaces and chooses search directions that are mutually \(A\)-conjugate: \(p_i^TAp_j=0\) for \(i\ne j\).
• Locally Optimal Block Preconditioned Conjugate Gradient
  • LOBPCG discovers eigenvalues along with eigenvectors and corrects \(AX-BX\Theta\), not \(b-Ax\).

    This sourcePrimary linear-system conjugate-gradient boundary. Verified 2026-08-26.

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Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://doi.org/10.6028/jres.049.044 ×1

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