Greebaum, AnneTrogdon, Tomli, hongdali2022-07-142022-07-142022-07-142022li_washington_0250O_24133.pdfhttp://hdl.handle.net/1773/48811Thesis (Master's)--University of Washington, 2022We review results from the literature on the conjugate gradient algorithm for solving symmetric positive definite linear systems and the related Lanczos algorithm. We derive the conjugate gradient algorithm from the more general conjugate directionmethod, using projectors. We establish error bounds using exact arithmetic theory and also discuss what can happen when floating-point arithmetic is used. We present numerical experiments to illustrate this behavior.application/pdfen-USCC BYconjugate gradientfloating-point arithmeticlanczos algorithmnumerical analysisnumerical linear algebrasymmetric eigenvalue problemApplied mathematicsApplied mathematicsThesis