Original papers on conjugate gradient method and Lanczos iterations in NIST Journal of Research:
Magnus R. Hestenes and Eduard L. Stiefel, Methods of Conjugate Gradients for Solving Linear Systems, Journal of Research of the National Bureau of Standards, Vol. 49, No. 6, December 1952, pages 409-436. [Read Online].
Cornelius Lanczos, Solution of Systems of Linear Equations by Minimized Iterations, Journal of Research of the National Bureau of Standards, Vol. 49, No. 1, July 1952, pages 33-53. [Read Online]
Cornelius Lanczos, An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators, Journal of Research of the National Bureau of Standards, Vol. 45, No. 4, October 1950, pages 255-282. [Read Online]