Theory and Applications: Numerical Analysis

Dear Colleagues,

We are pleased to invite you to contribute to this Special Issue. In today's era of rapid scientific and technological advancement, many fundamental questions in natural sciences, engineering, and social sciences can ultimately be reduced to solving mathematical models. However, real-world mathematical models often present significant complexity, with most lacking exact analytical solutions. Examples include fluid dynamics simulations in aerospace, molecular dynamics calculations in biomedicine, and risk assessment models in financial engineering—all of which require efficient numerical methods to overcome theoretical limitations. As a core interdisciplinary field bridging mathematics and computer science, numerical analysis focuses on developing computational approaches to solve mathematical problems. This discipline encompasses critical aspects such as algorithm design, error analysis, stability verification, convergence proofs, and efficiency optimization. With exponential growth in computing power, the advent of the big data era, and deepening interdisciplinary research, the applications of numerical analysis continue to expand. Its pivotal role as a bridge between theoretical models and practical implementations has become increasingly prominent, serving as a crucial foundation for driving technological innovation and scientific discoveries across various fields.

This Special Issue is dedicated to exploring the core and cutting-edge research directions in numerical analysis, featuring high-quality original research papers and review articles to compile a collection of at least 10 academic achievements. The theme strictly aligns with the scope of the journal Axioms, avoiding both excessive breadth and narrow focus. By providing a high-level platform for academic exchange and achievement display for researchers worldwide in related fields, it aims to advance the theoretical development and interdisciplinary practical applications of numerical analysis, thereby enhancing the field's influence in addressing major real-world challenges.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but not limited to) the following:

• Numerical Solutions of Linear Algebraic Equation System;
• Numerical Solutions of Nonlinear Algebraic Equation System;
• Algebraic eigenvalue problem;
• Efficient Numerical Solutions for Least Squares Problem;
• Theory and Application of Quaternions Matrix;
• Matrix decomposition;
• Efficient Computation Methods for Large Scale Matrix;
• Numerical optimization algorithms;
• Optimization methods;
• Numerical Solutions of Ordinary Differential Equation;
• Numerical Solutions of Partial Differential Equation;
• Calculation of Mathematical Physics Inverse Problem;
• Matrix Computation in Machine Learning and Deep Learning;
• Intelligent optimization algorithms.

We look forward to receiving your contributions.

Prof. Dr. Xinhui Shao
Dr. Hailong Shen
Dr. Guanyu Xue
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• solution methods for linear algebra systems
• solution methods for nonlinear algebra systems
• numerical methods for differential equations
• mathematical physics inverse problems
• matrix factorization
• matrix computation
• matrix analysis
• quaternion matrix theory
• stochastic algorithms
• intelligent optimization algorithms
• machine learning
• deep learning