Version 1.2.0

12th April 2013

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HSL_MI31 Symmetric positive-definite system: conjugate gradient method, stopping according to the A-norm of the error

The package uses the preconditioned conjugate gradient method to solve the n × n symmetric positive-definite linear system

Au = b,

and implements several stopping criteria based on lower and upper bounds of the A-norm of the error. If M = UTU is the preconditioning matrix, the routine actually solves the preconditioned system

ĀY = b̄,

with Ā = UTAU1 and b̄ = UTb and recovers the solution u = U1y.

Reverse communication is used. Control is returned to the user for preconditioning operations and the products of A with a vector z.