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math.NA2026
Running error bounds in finite element kernels
Michal Habera, Paul T. Kühner, Matteo Croci +1
Rounding errors in finite element computations can lead to a complete loss of accuracy, stalled convergence, and incorrect results. Moreover, the effects of rounding errors accumul…
math.NA2025★ 1 cited
Numerically stable evaluation of closed-form expressions for eigenvalues of matrices
Michal Habera, Andreas Zilian
Trigonometric formulas for eigenvalues of matrices that build on Cardano's and Viète's work on algebraic solutions of the cubic are numerically unstable for matrices w…
math.NA2021
Symbolic spectral decomposition of 3x3 matrices
Michal Habera, Andreas Zilian
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrice…