The paper introduces minimal residual multistep (MRMS) methods that adapt explicit multistep coefficients to minimize a BDF residual, reducing per-step linear algebra to a thin least-squares solve while preserving the order and zero-stability of the underlying BDF formula.
Saad, Iterative Methods for Sparse Linear Systems, 2nd Edition, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2003
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Minimal residual multistep methods for large stiff non-autonomous linear problems
The paper introduces minimal residual multistep (MRMS) methods that adapt explicit multistep coefficients to minimize a BDF residual, reducing per-step linear algebra to a thin least-squares solve while preserving the order and zero-stability of the underlying BDF formula.