Serveless-Based High-Dimensional Matrix Operations and Their Financial Applications

This paper systematically analyzes multivariate methods for high-dimensional matrix computation and their optimization strategies for applications in finance. At the level of high-dimensional computation, it focuses on the technical characteristics of direct methods , iterative methods , and randomized algorithms , which reveal their efficiency gains in financial derivatives pricing, risk matrix modeling, and other scenarios. For serverless architecture, the study focuses on its core advantages of elastic scaling and on-demand billing, through parallel task slicing and cost optimization, while analyzing the limitations of its stateless design on the adaptation of iterative algorithms and the constraints of cold-start latency on high-frequency trading. In addition, the article delves into the special challenges of financial modeling, including the cubic complexity pressure of high-dimensional operations, real-time conflicts of missing data interpolation, and privacy compliance requirements, and discusses hybrid architectures (serverless with local GPU synergy) and middleware (Redis, AWS Step Functions) as the current transitional solutions for balancing efficiency and state. The research also addresses the challenges of nonlinear dynamic modeling and interpretability requirements for machine learning-driven models, providing a multidimensional analytical framework for technology adaptability.