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In theory, the successive gradients generated by the conjugate gradient method applied to a quadratic should be orthogonal. However, for some ill-conditioned problems, orthogonality is quickly lost due to rounding errors, and convergence is much slower than expected. A limited memory version of the nonlinear conjugate gradient method is developed. The memory is used to both detect the loss of orthogonality and to restore orthogonality. An implementation of the algorithm is presented based ondoi:10.1137/120898097 fatcat:gkj6phzstbejlpj3du3kysbm6m