Abstract
An iterative algorithm based on the critical descent vector is pro- posed to solve an ill-posed linear system: Bx = b. We define a future cone in the Minkowski space as an invariant manifold, wherein the discrete dynamics evolves. A critical value ac in the critical descent vector u = acr+ B T r is derived, which renders the largest convergence rate as to be the globally optimal iterative al- gorithm (GOIA) among all the numerically iterative algorithms with the descent vector having the form u = ar+ B T r to solve the ill-posed linear problems. Some numerical examples are used to reveal the superior performance of the GOIA.
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