Numerical computation 1

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This book explores various facets of scientific numerical computing without aiming for completeness or an encyclopedic approach. The successful resolution of numerical problems involves multiple aspects of computer science, distinguishing computer numerics from computer algebra. It draws on applied mathematics, numerical analysis, numerical computation, and specific areas of computer science, including computer architecture and operating systems. Each chapter starts with practical examples from specific application fields, followed by abstract formulations of mathematical problems. A general discussion on principles and methods for numerically solving these problems is provided, alongside the development of relevant algorithms, assessing their efficiency and accuracy. The text explains how these algorithms can be transformed into numerical software. Readers are guided on applying general methods and principles to specific problem classes, focusing on extracting practically useful solutions through appropriately selected numerical software. The book also addresses potential challenges and obstacles, offering strategies to overcome them. The breadth and variety of available numerical software are substantial, reflecting the complexity of the field.