Adaptive Nonlinear Discriminant Analysis by Regularized Minimum Squared Errors
IEEE Transactions on Knowledge and Data Engineering
Systolic Algorithms and Architectures for High-Throughput Processing Applications
Journal of Signal Processing Systems
Online Sparse Matrix Gaussian Process Regression and Vision Applications
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Modified Gram-Schmidt-based methods for block downdating the Cholesky factorization
Journal of Computational and Applied Mathematics
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Solutions to a sequence of modified least squares problems, where either a new observation is added (updating) or an old observation is deleted (downdating), are required in many applications. Stable algorithms for downdating can be constructed if the complete QR factorization of the data matrix is available. Algorithms that only downdate $R$ and do not store $Q$ require less operations. However, they do not give good accuracy and may not recover accuracy after an ill-conditioned problem has occurred. The authors describe a new algorithm for accurate downdating of least squares solutions and compare it to existing algorithms. Numerical test results are also presented using the sliding window method, where a number of updatings and downdatings occur repeatedly.