Introduction to Numerical Mathematics - Richter, Thomas

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Résumé :

Introduction.- Part I Numerical Methods of Linear Algebra.- Fundamentals of Linear Algebra.- Linear Systems.- Orthogonalization Methods and QR Factorization.- The Eigenvalue Problem.- Krylov Subspace Methods.- Part II ...

Biographie:

This textbook presents the theoretical foundations of numerical mathematics in a modern, application-oriented, and comprehensive way. In addition to the standard content, it includes numerous examples and practical excursions to sustainably enhance understanding. Proofs are presented in a very detailed, step-by-step manner. The recurring core concepts of numerical mathematics like accuracy, efficiency, robustness and stability are explicitly addressed and clearly distinguished from one another. Specific example calculations for the described algorithms are carried out using provided Python codes. Numerical modeling for aspects of machine learning and neural networks are taken into consideration. Furthermore, numerical methods from linear algebra and analysis are presented separately, which significantly facilitates students&rsquo...

Sommaire:
Numerical Methods of Analysis.- Fundamentals of Calculus.- Root Finding Problems.- Interpolation and Approximation.- Numerical Integration.- Mathematical Optimization and Artificial Neural
Networks.