Krylov subspace accelerated inexact Newton method for linear and nonlinear equations
Related Experiment Video
Updated: Aug 29, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
Published on: October 28, 2022
1Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Mail Stop K1-96, P.O. Box 999, Richland, Washington 99352, USA. harrisonrj@ornl.gov
Abstract:
A Krylov subspace accelerated inexact Newton (KAIN) method for solving linear and nonlinear equations is described, and its relationship to the popular direct inversion in the iterative subspace method [DIIS; Pulay, P., Chem Phys Lett 1980, 393, 73] is analyzed. The two methods are compared with application to simple test equations and the location of the minimum energy crossing point of potential energy surfaces. KAIN is no more complicated to implement than DIIS, but can accommodate a wider variety of preconditioning and performs substantially better with poor preconditioning. With perfect preconditioning, KAIN is shown to be very similar to DIIS. For these reasons, KAIN is recommended as a replacement for DIIS.
Related Concept Videos
Newton’s Method
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Linearization and Approximation
Systems of Linear Equations in Two Variables
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.