AWhat changed
Golub and Kahan develop a two-stage scheme that reduces a rectangular matrix to bidiagonal form, then computes its singular values and paired vectors for pseudoinverse and least-squares calculations.
Scientific scope
Golub and Kahan develop a two-stage scheme that reduces a rectangular matrix to bidiagonal form, then computes its singular values and paired vectors for pseudoinverse and least-squares calculations. The target is the stated bidiagonalization and singular-value computation for finite matrices. Reduction, iterative diagonalization, convergence/stopping and floating-point behavior are distinct steps. Exact orthogonal transformations do not guarantee accurate small singular values under every numerical condition. Later stable implementations and performance improvements remain separate.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Gene Golub · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- William Kahan · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- G. Golub and W. Kahan, Calculating the Singular Values and Pseudo-Inverse of a Matrix (1965), author-posted original
- SIAM original target bibliography and publication/submission history for Golub-Kahan 1965
- Stanford-hosted Trefethen classic numerical-paper list and 1993 course account
- William Kahan institutional author homepage: target 1965 publication
- Gene Golub institutional course header and numerical linear algebra topics
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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