New Taylor method for the matrix sign function

Emilio Defez, José Miguel Alonso, Javier Ibáñez and Jorge Sastre present a new Taylor-based method for computing the matrix sign function at MME&HB 2026.

The matrix sign function is an important tool in numerical linear algebra, with applications to the solution of matrix equations and matrix decomposition problems. Its efficient computation remains an interesting challenge, particularly when accuracy and computational cost must be considered together.

Building on the research group’s experience in polynomial approximation and efficient matrix polynomial evaluation, the authors introduce a new approach within the family of Taylor methods for this function. The contribution extends their ongoing work on polynomial-based algorithms for matrix functions, exploring how Taylor approximations can provide an alternative framework for their numerical computation.

The proposed method adds to the group’s research into efficient algorithms for matrix functions, with a particular focus on developing numerical techniques that combine mathematical accuracy with practical computational efficiency.

Publication Details

  • Title: A new Taylor method for the matrix sign function
  • Authors: Emilio Defez, José Miguel Alonso, Javier Ibáñez, Jorge Sastre
  • Conference: Mathematical Modelling in Engineering & Human Behaviour 2026 (MME&HB 2026), Valencia, July 12–15 of 2026
  • Proceedings: Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, pp. 356–363
  • ISBN: 978-84-09-89823-7
  • Enlace: https://imm.webs.upv.es/jornadas/2026/2026_Proceedings_MME_HB.pdf

Main Contributions

  • A new method based on Taylor series for the matrix sign function.
  • An alternative within the set of polynomial techniques for this function.
  • A connection with the group’s research on efficient matrix polynomial evaluation.

Why This Matters

The matrix sign function arises in control problems, the solution of Riccati equations, and the computation of other matrix functions. An additional Taylor method broadens the range of available algorithmic approaches.