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Once again, consider the use of DNN for classification task with the specific architecture below that we have encounter...
Problem 2. In this problem we consider the question of whether a small value of the residual kAz − bk means that z is a good approximation to the solution x of the linear system Ax = b. We showed in class that, kx − zk kxk ≤ kAkkA −1 k kAz − bk kbk . which implies that if the condition number kAkkA−1k of A is small, a small relative residual implies a small relative error in the solution....
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system to be an "object" along with a specific set of modifications that can be performed (dynamically) upon this object. In this case, the object is a bi-infinite straight road with a lamp post at every street corner and a marked lamp (the position of the lamplighter). There are two possible types of modifications: the lamplighter can walk any distance in either direction from...