TY - JOUR A1 - Hanke, Michael A1 - März, Roswitha A1 - Tischendorf, Caren T1 - Least-Squares Collocation for Higher-Index Linear Differential-Algebraic Equations: Estimating the Instability Threshold JF - Math. Comp. N2 - Differential-algebraic equations with higher index give rise to essentially ill-posed problems. The least-squares collocation by discretizing the pre-image space is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations and index-1 differential-algebraic equations. This approach has displayed excellent convergence properties in numerical experiments, however, theoretically, till now convergence could be established merely for regular linear differential-algebraic equations with constant coefficients. We present now an estimate of the instability threshold which serves as the basic key for proving convergence for general regular linear DAEs. KW - differential-algebraic equation, higher index, essentially ill-posed problem, collocation, boundary value problem, initial value problem Y1 - 2017 U6 - https://doi.org/10.1090/mcom/3393 VL - 88 SP - 1647 EP - 1683 ER -