We present a reduced basis method for parametrized linear elliptic partial differential equations (PDEs) in least-squares finite element framework. A rigorous and reliable error estimate is developed, shown to bound the with respect exact solution of PDE, contrast estimates that measure finite-dimensional (high-fidelity) approximation. It first-order formulation key ingredient. The demonstrated...

The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...