The ResQPASS algorithm solves linear least squares with bound constraints efficiently by projecting onto residuals and using active-set methods. It converges like CG and LSQR when few constraints are active, showing promise for large-scale problems.
The paper introduces an efficient implementation updating QR factorizations over iterations and Cholesky factorizations over outer iterations. The method's convergence is linked to Krylov theory, offering insights into solving bounded-variable least squares problems effectively.
Key contributions include warm-starting capabilities, Cholesky factorization updates, and limiting inner iterations for optimal performance. The algorithm's recursive relationships improve efficiency, while stopping criteria ensure accurate solutions within specified tolerances.
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