Discuss the computational cost of the preconditioning

The gap

Evidence profile

Sourced from the stated research gap and future-work section and limitations section of the source papers, classified as general, spanning 4 journals.

Supporting evidence — 6 representative gaps

• A priori error estimates of a fictitious domain formulation of the Newtonian cooling problem (2026) · BIT Numerical Mathematics · doi

  The lack of a priori error estimates for the fictitious domain formulation. The need for a comprehensive analysis of the numerical results. The need for a preconditioning strategy for the extended system.

  generalstated research gapevidence 5/5
  Keywords: lack priori error estimates fictitious domain formulation need
• A priori error estimates of a fictitious domain formulation of the Newtonian cooling problem (2026) · BIT Numerical Mathematics · doi

  Further analysis of the numerical results is needed. The application of the fictitious domain formulation to other problems is a potential future research direction. The development of more efficient preconditioning strategies is a potential future research direction.

  generalfuture-work sectionevidence 5/5
  Keywords: further analysis numerical results needed application fictitious domain
• An Augmented Lagrangian Preconditioner for Navier–Stokes Equations With Runge–Kutta in Time (2026) · Numerical Linear Algebra with Applications · doi

  The need for a fast and robust preconditioner for the Newton systems arising at each time step. The lack of a rigorous theoretical analysis of the proposed method.

  generalstated research gapevidence 5/5
  Keywords: need fast robust preconditioner newton systems arising each
• Preconditioning Transformations of Adjoint Systems for Evolution Equations (2026) · Journal of Nonlinear Science · doi

  To apply the framework to other types of equations. To investigate the computational cost of the preconditioning transformation. To explore the application of the framework to various fields.

  generalfuture-work sectionevidence 5/5
  Keywords: apply framework other types equations investigate computational cost
• Any Nonincreasing Convergence Curves are Simultaneously Possible for GMRES and Weighted GMRES, As Well As for Left and Right Preconditioned GMRES (2026) · Foundations of Computational Mathematics · doi

  To further investigate the properties of weighted GMRES. To explore the applications of the paper's results in practice. To develop more efficient preconditioning strategies based on the paper's results.

  generalfuture-work sectionevidence 5/5
  Keywords: further investigate properties weighted gmres explore applications paper
• Preconditioning Transformations of Adjoint Systems for Evolution Equations (2026) · Journal of Nonlinear Science · doi

  The paper does not discuss the computational cost of the preconditioning transformation. The numerical example is limited to a specific problem.

  generallimitations sectionevidence 4/5
  Keywords: paper does discuss computational cost preconditioning transformation numerical

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