想要深入了解数值线性代数在偏微分方程、机器学习和数据同化中的应用？这本书是绝佳的选择，它不仅介绍了经典算法，还展示了这些算法在现代科学和工程中的重要性。
本课程笔记是高级数值线性代数硕士课程的第一个部分，旨在展示该主题为何比一代人前变得更加核心。内容涵盖从范数、因子分解、条件数和浮点运算到稀疏矩阵、迭代方法和预处理的各个方面。每章都包含总结和练习。
Advanced Linear Algebra with Applications - Part I (Numerical linear algebra for PDEs, machine learning, and data assimilation)
These lecture notes form the first part of a master's-level course on advanced numerical linear algebra. Their aim is not only to present the classical algorithms, but to show why the subject has become considerably more central than it was a generation ago. Numerical linear algebra grew up alongside the numerical solution of partial differential equations, and for a long time that is where its large sparse systems came from. Ranking the nodes of a network, assimilating observations into a weather forecast, and fitting a model to a large noisy data set now lead to problems of the same kind: too large to factorise, structured, and accessible only through matrix-vector products. Strikingly few ideas are needed for all of them. Each chapter therefore develops a standard topic and then puts it to work outside its original setting. We treat norms, factorisations, conditioning and floating-point arithmetic; sparse matrices arising from finite differences, from graphs and from machine learning; stationary iterations and the smoothing property; the conjugate gradient and Lanczos methods, with spectral clustering and regularisation by early stopping; Arnoldi and GMRES, with PageRank and large least squares; and finally preconditioning, Schwarz domain decomposition and multigrid. We assume a first course in linear algebra. Every section closes with a summary of what should be retained and every chapter with exercises, several drawn from past examinations. Accompanying Python code reproduces the numerical illustrations.