# CPSC 402 Test #1 Topics

The test will cover Chapter 1, Sections 1.1 - 1.3 (plus Horner's method for evaluating polynomials and basic calculus results such as the approximation of the derivative, Taylor polynomials, etc.) and Chapter 2, Sections 2.1, 2.2, 2.3 (through page 58, not including ways to estimate the norm of the inverse of a matrix), Section 2.4 (up through the first paragraph on page 76) plus the scaled partial pivoting algorithm (which is not explicitly discussed in the text).

The main ideas are:

• Error: Absolute/Relative, Truncation/Round-off, Computational/Data; Forward/Backward; sources of error, means of approximating error
• Sensitivity and Conditioning of a problem: what it means, measurement using the condition number (definition and approximation)
• Stability/Accuracy of an algorithm
• Computer representation of numbers and properties of a given representation (UFL, OFL, machine epsilon, subnormals)
• Floating Point Arithmetic: how it works, how/when error arises, detecting when error may arise, methods of revising the algorithm to avoid error as much as possible
• Linear Algebra -- basic properties and terminology
• Gaussian elimination -- under what circumstances is basic Gaussian elimination (without pivoting) unstable? what pivoting strategies are more stable?
• Ill-Conditioned Systems: be able to detect by observation in simple cases (nearly singular), understand that the determinant cannot be used to detect, know how to compute norms and the condition number, know what the condition number tells you about the system.

### Suggested Review Problems and Exercises from the Text

• Chapter 1 Review Questions #1.1 - 1.46, 1.50, 1.51
• Chapter 1 Exercises #1.1 - 1.12. 1.19, 1.20, 1.22, 1.23
• Chapter 2 Review Questions #2.2, 2.4, 2.5, 2.14, 2.18, 2.22, 2.25, 2.34, 2.35, 2.37 - 2.40, 2.52 - 2.57, 2.59, 2.61, 2.62, 2.64, 2.65
• Chapter 2 Exercises #2.7, 2.17, 2.33

Answers to Selected Review Questions and Exercises will be posted on the bulletin board outside Trexler 365 on Monday.