This preview shows page 1. Sign up to view the full content.
Unformatted text preview: αt tr(∇f0 (X )∆X )
is satisﬁed. To check that a matrix X + t∆X is positive deﬁnite, you can use the Cholesky
factorization with two output arguments ([R, p] = chol(A) returns p > 0 if A is not positive
Test your code on randomly generated problems of sizes n = 10, . . . , 100 (for example, using
n = 100; C = randn(n); C = C + C’).
8.9 Estimation of a vector from one-bit measurements. A system of m sensors is used to estimate an
unknown parameter x ∈ Rn . Each sensor makes a noisy measurement of some linear combination
of the unknown parameters, and quantizes the measured value to one bit: it returns +1 if the
measured value exceeds a certain threshold, and −1 otherwise. In other words, the output of
sensor i is given by
1 a T x + v i ≥ bi
yi = sign(aT x + vi − bi ) =
− 1 a T x + v i < bi ,
where ai and bi are known, and vi is measurement error. We assume that the measurement errors
vi are independent random variables with a zero-mean unit-variance Gaussian distribution (i.e.,...
View Full Document
This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
- Fall '13
- The Aeneid