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Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. II: The discrete least-squares problem. (English) Zbl 1484.65165

Summary: In the two parts of the present note we discuss questions concerning the implementation of overdetermined least-squares collocation methods for higher index differential-algebraic equations (DAEs). Since higher index DAEs lead to ill-posed problems in natural settings, the discrete counterparts are expected to be very sensitive, which attaches particular importance to their implementation. We provide in Part 1 [the authors, ibid. 89, No. 3, 931–963 (2022; Zbl 1484.65164)] a robust selection of basis functions and collocation points to design the discrete problem whereas we analyze the discrete least-squares problem and substantiate a procedure for its numerical solution in Part 2.

MSC:

65L80 Numerical methods for differential-algebraic equations
65L08 Numerical solution of ill-posed problems involving ordinary differential equations
65F20 Numerical solutions to overdetermined systems, pseudoinverses
34A09 Implicit ordinary differential equations, differential-algebraic equations

Citations:

Zbl 1484.65164
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References:

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