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math.OC2014★ 1 cited
On solving symmetric systems of linear equations in an unnormalized Krylov subspace framework
Anders Forsgren, Tove Odland
In an unnormalized Krylov subspace framework for solving symmetric systems of linear equations, the orthogonal vectors that are generated by a Lanczos process are not necessarily o…
math.OC2014★ 4 cited
On the connection between the conjugate gradient method and quasi-Newton methods on quadratic problems
Anders Forsgren, Tove Odland
It is well known that the conjugate gradient method and a quasi-Newton method, using any well-defined update matrix from the one-parameter Broyden family of updates, produce identi…
math.OC2014★ 1 cited
An elementary proof of linear programming optimality conditions without using Farkas' lemma
Anders Forsgren, Margaret H. Wright
Although it is easy to prove the sufficient conditions for optimality of a linear program, the necessary conditions pose a pedagogical challenge. A widespread practice in deriving…