The field of function approximation and image analysis is moving towards the development of more efficient and accurate methods for solving complex problems. Researchers are exploring new approaches to linear algebra and convolution operators to improve the accuracy of function approximation and image analysis. The use of tensor neural networks and frequency-adaptive algorithms is also becoming increasingly popular for solving high-dimensional multi-scale problems. Notable papers in this area include:

• A study on dimension lower bounds for linear approaches to function approximation, which presents a linear algebraic approach to proving dimension lower bounds for linear methods.
• A paper on frequency-adaptive tensor neural networks for high-dimensional multi-scale problems, which proposes a novel approach to extract frequency features of high-dimensional functions.