This function is shown below. Now suppose you are given measured runtimes for N executions of the algorithm, with different sets of input data. Your method should have the property that f x k converges to y as k increases. As usual, we assume that smaller values of kvk are more plausible than larger values. In that case you obtained the quadratic extrapolator by interpolating the last three samples; now you are obtaining it as the least squares fit to the last ten samples. We give it so you can see how well or poorly the smoothing does. To convince us of this, give a specific example, where the collection of subsets is informative, but the method above fails, i.

The path gain from transmitter j to receiver i is Gij which are all nonnegative, and Gii are positive. The roughness measure R is zero precisely for constant arrays, i. Plot c, d, and w, and r. There are some slight differences when it comes to the inner product and other expressions that, in the real case, involve the transpose operator. We will think of the index i as associated with the y axis, and the index j as associated with the x axis. In the lecture notes, you can see a plot of the least Euclidean norm force profile. But you must state this clearly.

A group of statements is equivalent if any pair of statements in the group is equivalent. Give the RMS value of the prediction error obtained with your coefficients. If your method requires some matrix or matrices to be full rank, say so.

In general, however, it is an extremely difficult problem to compute a least-norm solution to a set of nonlinear equations.

When the output of gate i is connected to an input of gate j, we say that gate i drives gate j, or that gate j is in the fan-out of gate i. Such a function is called a rational function of degree m.

# Ee homework 1 solutions

Note that both of these are given in degrees, not radians. Note that increasing pi t power of the ith transmitter increases Si but decreases all other Sj.

Still, you can solve it with material we have covered. There is no such thing as a nonlinear unbiased estimator.

## Ee263 homework 1 solutions

This problem explores a famous heuristic method, based on solving a sequence of linear ee2263 problems, for finding coefficients a, b that approximately minimize J. Be sure to explain why the algorithm you describe cannot fail. In this problem, you should think of the index for y as denoting a time period, and you should imagine the measurements i. The vehicle starts at the origin, at rest, i.

Find the fastest way to get a message that starts at node solutione, to node You can assume that all of the matrices are full rank, i.

To get a feel for the heating system, we recommend that you try out various powers to see the resulting temperature profile. For example, all the external flow entering node 2 goes to node 1, then to the destination node. Using this representation we will use the following objectives, provlems approximate the ones defined for the functions above: The reaction R1 has no effect on metabolites M4.

The amounts we purchase are large enough to have a noticeable effect on the price of the shares.

# EE homework 5 solutions

In other words, multiplication by such a matrix preserves norm. We require that the estimator be unbiased, i. Try to use the simplest notation you can. We start with the discrete-time model of the system used in lecture 1: The prediction error depends on the time-series data, and also A, the parameter in our model. Do not mention the incident to anyone.

## EE263 homework 5 solutions

Find uss and xss. You may assume that the norm of the least-squares approximate solution exceeds one, i.

These methods, along with some informal justification from their proposers, are given below. You will develop several different models that relate the signals u and y. We call the collection of subsets S1. First verify the following inequality, which is like the Cauchy-Schwarz inequality but even easier to prove: This priblems the Fourier transform and other signal processing methods you might know.

In the first, you simply generalize all the results to work for complex matrices, vectors, and scalars. One situation where this problem comes up is a nonstandard filtering or equalization problem.