The sequence of Givens rotations used to update the upper triangular matrix R in a recursive QR decomposition may also be used to update the inverse transpose matrix R$+$MIN@H$/. Alternative forms of square-root-free Givens rotation for updating the inverse transpose matrix are derived by representing and storing it in a different factorized form from that used before. The modified Givens rotations do not involve explicit division by the exponential forget factor and lead to an update algorithm equivalent to the one derived by Sakai using Recursive Modified Gram Schmidt orthogonalization.
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机译：用于更新递归QR分解中的上三角矩阵R的Givens旋转的序列也可以用于更新逆转矩阵r $ + $ min @ h $ /。通过表示和将其存储在之前使用的不同的分解形式中，导出用于更新逆转矩阵的替代形式的用于更新逆转矩阵的旋转。修改的GIVENS旋转不涉及指数忘记因子的显式划分，并导致使用Sakai使用递归修改的Gram Schmidt正交化的更新算法。
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