Can I read Chapter 3: Experimental accuracy analysis on EtoBox?

Chapter 3: Experimental accuracy analysis by Brian Sutton is a book available to read on EtoBox.

What is Chapter 3: Experimental accuracy analysis about?

Because exact solution formulas do not exist for many problems, our numerical methods are typically indirect. One common approach is to express a desired quantity as a limit of a sequence: x D lim n!1 x n . As the sequence is traversed, the terms get closer and closer to the desired answer. Rather than taking the limit n ! 1, many of our numerical methods stop at some large n. The resulting error is called truncation error. Commonly available computers store real numbers to about 15 or 16 digits of precision. For this reason, a sequence of approximations may settle on a fixed value rather than becoming forever more accurate. When this happens, we say that numerical convergence has occurred. This often indicates that high accuracy has been achieved. This chapter presents a number of examples in which numerical convergence is sought and rate of convergence is measured empirically. These experimental techniques can justify high confidence in the accuracy of computations, and in later chapters, they are complemented by rigorous proofs.

Author

Brian Sutton

Publisher

SIAM - Society for Industrial and Applied Mathematics

Published

2019

Language

EN

ISBN

9781611975703

Subjects

Mathematics, Stem