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