2nd Edition. — Transl. from the Hungarian. — Springer/Birkhauser, 2024. — 308 p. — (Compact Textbooks in Mathematics). — ISBN 978-3-031-66088.
This book covers the basics of numerical methods. Avoiding the definition-theorem-proof style, it instead focuses on numerical examples and simple pseudo-codes. The text begins with a chapter on floating point arithmetic before moving on to discuss norms, conditions numbers, solutions of systems of equations, the least squares problem, eigenvalue problems, interpolation, numerical integration, ordinary differential equations, optimization (including a detailed case study), and practical error estimations. Exercises (partly in MatLAB) are provided at the end of each chapter. Suitable for readers with minimal mathematical knowledge, the book not only offers an elementary introduction to numerical mathematics for programmers and engineers but also provides supporting material for students and teachers of mathematics.
Floating Point Arithmetic
Norms: Condition Numbers
Solving Systems of Linear Equation
The Least Squares Problem
Eigenvalue Problems
Interpolation
Nonlinear Equations and Systems
Numerical Integration
Numerical Solution of Ordinary Differential Equations
Optimization
Practical Error Estimation for Discretized Models
References