Numerical Computation 1

1. Front Matter

   Pages I-XVI

   PDF

2. Scientific Modeling

   • Christoph W. Ueberhuber

   Pages 1-8

3. Fundamental Principles of Numerical Methods

   • Christoph W. Ueberhuber

   Pages 9-67

4. Computers for Numerical Data Processing

   • Christoph W. Ueberhuber

   Pages 68-105

5. Numerical Data and Numerical Operations

   • Christoph W. Ueberhuber

   Pages 106-171

6. Numerical Algorithms

   • Christoph W. Ueberhuber

   Pages 172-218

7. Numerical Programs

   • Christoph W. Ueberhuber

   Pages 219-271

8. Available Numerical Software

   • Christoph W. Ueberhuber

   Pages 272-307

9. Using Approximation in Mathematical Model Building

   • Christoph W. Ueberhuber

   Pages 308-352

10. Interpolation

    • Christoph W. Ueberhuber

    Pages 353-439

11. Back Matter

    Pages 440-477

    PDF

This book deals with various aspects of scientific numerical computing. No at­ tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli­ cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous.

• Analysis
• Numerical integration
• Transformation
• algorithm
• algorithms
• architecture
• complexity
• computer
• model
• modeling
• numerical analysis
• numerical methods
• numerics
• optimization

"The two volumes can be highly recommended for newcomers in the area as well as for people working for a long time in or with computer numerics." - EUROSIM - Simulation News Europe

"...This book is highly recommended to students, scientists, and engineers interested in the numerical solution of mathematical problems. It is very useful as a handbook for both newcomers and experts. Every science/engineering\-/mathematics/computer science library should have a copy of this book."--MATHEMATICAL REVIEWS

• Technical University of Vienna, Vienna, Austria

  Christoph W. Ueberhuber

Policies and ethics