Approximation theory is a deep theoretical study of methods that use numerical approximation for the problems of mathematical analysis. In practical use, it is typically the application of computer simulation and other forms of computation to problems in various scientific disciplines. Recently, numerical algorithms in approximation theory have been a major thrust of research with numerous applications.

In this special issue, we solicit original works in all areas of computational science whose areas is in the domain of approximation theory. In particular, we seek original work on identifying new research and development challenges and developing new techniques and algorithms in numerical analysis. Hence, this special issue is intended to present recent trends and advances of analytical and numerical methods for all aspects involved in approximation theory.

Potential topics include, but are not limited to:

• Iterative methods for sparse linear systems
• Novel algorithms for matrix inversion
• New schemes with and without memory for solving nonlinear equations or systems
• Iterative methods for solving nonlinear matrix equations
• New methods for computing special matrix functions
• Recent developments in numerical solution of ODEs, PDEs, FDEs, SDEs, and IEs
• Approximation theory
• Numerical methods in chaos: periodic, chaotic, and hyperchaotic solutions
• Others and emerging new topics