09-23-2026, 04:35 PM
Numerical Mathematics by Jeffrey Ovall is a 2024 SIAM textbook that develops the theory and practice of numerical methods for scientific computing. It is organized into three major areas: numerical calculus, numerical differential equations, and numerical linear algebra.
The book begins with approximation, convergence rates, error analysis, and floating-point arithmetic, then covers nonlinear equations, polynomial interpolation, numerical differentiation and integration, initial- and boundary-value problems, and the 2D Poisson equation. A recurring theme is connecting the mathematical theory of an algorithm—especially its accuracy and convergence—with its actual computational performance.
The final part focuses on numerical linear algebra, including matrix decompositions and direct methods for linear systems, least-squares problems, and eigenvalue computations. Ovall also includes several topics that are less commonly emphasized in introductory texts, such as Fourier analysis of the trapezoidal rule, finite-volume methods for the 2D Poisson problem, the Nyström method for integral equations, and the FEAST eigenvalue algorithm.
With more than 600 pages, numerous computational examples, theoretical justifications, and exercises, the book is designed primarily for advanced undergraduates and beginning graduate students, while also serving as a foundation for researchers and students in scientific computing and applied mathematics.
BOOK
The book begins with approximation, convergence rates, error analysis, and floating-point arithmetic, then covers nonlinear equations, polynomial interpolation, numerical differentiation and integration, initial- and boundary-value problems, and the 2D Poisson equation. A recurring theme is connecting the mathematical theory of an algorithm—especially its accuracy and convergence—with its actual computational performance.
The final part focuses on numerical linear algebra, including matrix decompositions and direct methods for linear systems, least-squares problems, and eigenvalue computations. Ovall also includes several topics that are less commonly emphasized in introductory texts, such as Fourier analysis of the trapezoidal rule, finite-volume methods for the 2D Poisson problem, the Nyström method for integral equations, and the FEAST eigenvalue algorithm.
With more than 600 pages, numerous computational examples, theoretical justifications, and exercises, the book is designed primarily for advanced undergraduates and beginning graduate students, while also serving as a foundation for researchers and students in scientific computing and applied mathematics.
BOOK
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