A set of vectors

Assignment Help Mathematics
Reference no: EM13709284

Suppose that we are given a set of vectors {x(1),...,x(p)}, x(i) n, i = 1,...,p. Find the vector x n such that the average squared distance (norm) between and x(1),..., x(p),

is minimized. Use the SOSC to prove that the vector found above is a strict local minimizer. How is related to the centroid (or center of gravity) of the given set of points {x(1),...,x(p)}?"

"Prove the following generalization of the second-order sufficient condition:
Theorem: Let Ω be a convex subset of n, f 2 a real-valued function on Ω, and x* a point in Ω. Suppose that there exists c , c > 0, such that for all feasible directions d at x* (d ≠ 0), the following hold:
1. d∇f(x*) ≥ 0.
2. dF(x*)d ≥ c||d||2.
Then, x* is a strict local minimizer of f."

Reference no: EM13709284

Questions Cloud

A large company requires allegiance to no specific creed : During six years working for GMA, Jetson's Buddhism was never really an issue, and why would it be? Serving as the marketing director for a large company requires allegiance to no specific creed.
The most famous hominin fossil named lucy : 1. The most famous hominin fossil named lucy is the most studied examples of A. Austtralopithecus robustus B. Austtralopithecus garhi C. Australopithecus afarensis D. Australopithecus bahrelghazali
Find equations for lines parallel or perpendicular : Given an equation of a line, find equations for lines parallel or perpendicular to it going through specified points. Find the appropriate equations and points from the table below. Simplify your equations into slope-intercept form.
Find the closures of the following sets : 1. Find the closures of the following sets: a). {1/n: n is a natural number} b).Q, the set of rational numbers c). {rEQ: r^2
A set of vectors : Suppose that we are given a set of vectors {x(1),...,x(p)}, x(i) n, i = 1,...,p. Find the vector x n such that the average squared distance (norm) between and x(1),..., x(p),
A dermatologist judged whether each womam : 39 women used skin cream for 22 weeks. At the end of the period, a dermatologist judged whether each womam exhibited skin improvement. The results show that 22 women improved. Do the data provide sufficient evidence to conclude that the cream w..
Triangle def has vertices with the coordinates : If triangle DEF has vertices with the coordinates D (9,-3), E(-6,3) and F(3,6), what are the verticles of triangle D' E' F' under the dilation with the scale factorof 2/3 and the center of the origin (0,0)?
A geometric sequence is a sequence of the form : (a) Recall that a geometric sequence is a sequence of the form a, ar, ar^2, ar^3, ... At the MATLAB command prompt (not in an M-File), create a for-loop which prints the first 7 terms of this sequence when r = 1/3, a = 1. Include the outpu..
Compute the speed of the plane with respect to the ground : You are on an airplane traveling 30° south of due west at 140 m/s with respect to the air. What is the speed of the plane with respect to the ground

Reviews

Write a Review

Mathematics Questions & Answers

  How many shoppers like cheerios or total

out of 500 randomly chosen grocery shoppers, 320 like cheerios and 380 like total. 275 of the grocery shoppers liked both cheerios and total.

  What does best rental charge per day

Barney was charged $123.00 for 3 days and 300 miles, while Mary was charged $216.00 for 5 days and 600 miles. What does Best Rental charge per day, for mileage?

  How fast is the radius of the balloon increasing

A spherical balloon is inflated with a gas at the rate of 500 cm3/min. How fast is the radius of the balloon increasing at the instant the radius is 30 cm?

  George and harry haygood are building contractors

George and Harry Haygood are building contractors

  How large should the squares cut from the corners

an open-top box is to be made by cutting small congruent squares from corners of a 30 x 30 sheet and bending it up to the sides. how large should the squares cut from the corners to make the box hold as much as possible?

  Find an example online of a graph used in real life

Find an example online of a graph used in real life. Please provide the link to the web page by using the link button in the editor.

  In analyzing hits by v-1 buzz bombs in world war ii south

in analyzing hits by v-1 buzz bombs in world war ii south london was subdivided into regions each with an area of

  A triangular pyramid begins with these

a triangular pyramid begins with these coordinatesp-1 2 0y2 3 0r-3 4 0a-2 1 5the pyramid is then reflected over the

  What is the airplanes speed relative to the ground

In what direction should the plane head to end up going due east? What is the airplane's speed relative to the ground?

  At the end of the day she has 177800 in the register how

a woman owns a small cash-only business in a state that requires her to charge 7 sales tax on each item she sells. at

  Describe how quadratic equations are important

describe how quadratic equations are important to a basketball player or a sniper. And give a real world example.

  Explain what the answer means in practical terms

The componets of v=180i+450j represent the respective number of one-day and three day videos rented from a video store. the componets of w=3i+2j represent the prices to rent the one day and three day videos,respectively

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd