On the rate of convergence of the preconditioned conjugate gradient method
Numerische Mathematik
A limited memory algorithm for bound constrained optimization
SIAM Journal on Scientific Computing
Topics in optimization and sparse linear systems
Topics in optimization and sparse linear systems
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A simple polynomial-time rescaling algorithm for solving linear programs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A randomized polynomial-time simplex algorithm for linear programming
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
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We consider the problem of solving a symmetric, positive definite system of linear equations.The most well-known and widely-used method for solving such systemsis the preconditioned Conjugate Gradient method.The performance of this method depends crucially on knowing a good preconditioner matrix.We show that the Conjugate Gradient method itself canproduce good preconditioners as a by-product. These preconditioners allow us to derive new asymptotic bounds on the timeto solve multiple related linear systems.