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In previous work, we have introduced the technique of relaxed power series computations. With this technique, it is possible to solve implicit equations almost as quickly as doing the operations which occur in the implicit equation. In this paper, we present a new relaxed multiplication algorithm for the resolution of linear equations. The algorithm has the same asymptotic time complexity as our previous algorithms, but we improve the space overhead in the divide and conquer model and the constant factor in the F.F.T. model.

**Subject descriptors: **mathematics of computing,
numerical analysis, multiple precision arithmetic