Hestenes and Stiefel: conjugate gradients for linear systems

What changed

Developed conjugate-gradient algorithms for SPD systems with finite-step exact-arithmetic properties.

Scientific scope

The record is the exact two-author 1952 joint paper. The authors document independent development and contributions by Lanczos, Rosser, Forsythe and Paige; finite-precision behavior, preconditioning and later Krylov methods remain separate.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact two-author 1952 joint paper. The authors document independent development and contributions by Lanczos, Rosser, Forsythe and Paige; finite-precision behavior, preconditioning and later Krylov methods remain separate.

Contributors

• Magnus R. Hestenes · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.
• Eduard Stiefel · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• NIST full text of conjugate-gradient paper
• NIST historical page for conjugate-gradient and Lanczos iterations

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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