Copyright 2005 by the Society for Industrial and Applied Mathematics This electronic version is for personal use and may not be duplicated or distributed.
Denition and Examples
Denition 13.1. Let A Rmn , B Rpq . Then the
Numerical aspects t-Digit Arithmetic. Examining numerical aspects. Given x R, dene the t-digit oating point, representation, ft (x) = 0. d1 d2 . . . dt 10e, where the digits, di, and the exponent, e, minimize |x ft (x)|. If ft (x) is not unique, round awa
Inner product spaces Inner product spaces Dened for a pair of elements of a vector space, x, y X , x, y
: X X R (or possibly C).
Dening properties: 1. x, x R, x, x 0 and x, x = 0 x = 0.
2. x, y = x, y , for all scalars, . 3. x, y + z = x, y + x, z . 4.
We now look at the problem of designing a controller to achieve a performance speci cation for all plants, P(s), in a set of plants, P. The previous sections have dealt with the questions of performance
ECE247 System Identi cation
1. This exercise is motivated by a discussion in Ljung. Consider a ltered random signal
1 X h(j) e(k
where h(j) is the pulse response of a discrete-time LTI lter. We will look at severa
Chapter 6 r r AX = b: The Minimum Norm Solution and the Least-Square-Error Problem
Like the previous chapter, this chapter deals with the linear algebraic equation problem AX = b. However, in this chapter, we impose addi
November 14, 1999 5:50 pm
Notes on Vector and Matrix Norms
These notes survey most important properties of norms for vectors and for linear maps from one vector space to another, and of maps norms induce between a vector space and its