Corrections of gradient errors in the interactions regions (IRs) of high energy colliders have traditionally been made by changing the strengths of quadrupoles that are common to both beams, such as the triplet quadrupoles. This article shows that magnetic errors in the IR quadrupoles that are no common to both beams, such as the matching quadrupoles, can have an important influence and, therefore, the correction should also include these quadrupoles. A correction based on twelve IR quadrupoles (common and no common) is presented and validated through MADX simulations. To estimate the strengths of this correction, the action and phase in the inter-triplet space, the space that separates the two triplets of the IR, are required. A novel method to estimate these quantities is also presented. The main sources of uncertainties in this novel method are identified and compared to the current method that uses two beam position monitor within the inter-triplet space. Finally, LHC experimental data is used to estimate the strengths of a twelve-quadrupole correction in the interaction region 1 of the LHC. The resulting correction is compared with a six-quadrupole correction estimated with another method called segment-by-segment (SBS).
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