1. Data points are correlated if the covariance matrix is diagonal

Covariance Matrices and Data Distributions

  1. Gauss-Seidel method converges for the following linear system

https://atozmath.com/CONM/GaussEli.aspx?q=GS2&q1=2`3x-y%2Bz%3D8%3B2x-4y-z%3D1%3B2x%2B2y-6z%3D4`GS2``1.25&dm=D&dp=4&do=1#PrevPart

  1. Given data points { (1, -1), (2, 2) }, what is the linear Lagrange interpolation function?

Lagrange Interpolation Polynomial Calculator - Online

  1. We can optimize the function f(x) = (x-1)(x-2)(x-3)(x4) on [1, 4] by using the golden ratio search.

na15_optimization.pdf

p.11

  1. In an upper triangular system, the last equation contains only one variable.

https://en.wikipedia.org/wiki/Triangular_matrix

  1. Suppose that the function f(x, y) represents the WiFi signal strength in the computer lab. We measured the signal at four corner positions P0=(0, 0), P1=(0, 1), P2=(1, 0), and P3=(1, 1). The measured signals are f(0, 0) = 20, f(0, 1) = 180, f(1, 0) = 120, and f(1, 1) = 200. Estimate f(0.2, 0.5) using the bilinear interpolation method.

Bilinear Interpolation Calculator

  1. We want to find the minimum value of a unimodal function f(x) on the interval [0, 2] using the Fibonacci Search method with the tolerance e=0.3 (Length of the last subinterval ). What is the number of steps (n-2)?

na15_optimization.pdf

p.23

n은 F_n > (b-a)/e 인 n 중 최소값을 찾는 거지만 step은 n-2라는 것에 유의

  1. We are given data points {(x, y)}={(-1, -2), (1, -1), (2, 2), (4, 5)} where y = f(x). Fit a polynomial function f(x)=Ax+B to the data using the Least-Squares method.

https://www.mathsisfun.com/data/least-squares-calculator.html

  1. What is the determinent of Hessian matrix of f(x, y) = 2xy+2x-x^2-2y^2?

https://www.wolframalpha.com/input?i=Hessian+matrix+2xy%2B2x-x^2-2y^2

  1. What is a gradient of f(x, y) = yx^2+3x+4 at (2, -1)?

gradient yx^2+3x+4, at(2,-1) - Symbolab