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Let q(x) = x² Ax+b²x+c, where [1 0 1 1 0200 3 A = b = 10 30 1 100 4 Use Python or MATLAB for all parts of this question. (a) (2 points) Calculate the condition number of the matrix A and hence find an upper bound to the rate of convergence of the steepest descent method. (b) (5 points) Use the steepest descent method to find the minimiser, starting from x0 = (2,2,2,2). Tabulate the values of x that you find. Your table should have columns: k, xk, f(xk), uk, ||uk||, λk, and 1(x^-1(x*) f)xk-1-f(x*) (c) (2 points) Confirm that your algorithm does find the true minimiser and that the rate of convergence of your iterations lies within the bounds calculated in part (a).

Let q(x) = x² Ax+b²x+c, where [1 0 1 1 0200 3 A = b = 10 30 1 100 4 Use Python or MATLAB for all parts of this question. (a) (2 points) Calculate the condition number of the matrix A and hence find an upper bound to the rate of convergence of the steepest descent method. (b) (5 points) Use the steepest descent method to find the minimiser, starting from x0 = (2,2,2,2). Tabulate the values of x that you find. Your table should have columns: k, xk, f(xk), uk, ||uk||, λk, and 1(x^-1(x*) f)xk-1-f(x*) (c) (2 points) Confirm that your algorithm does find the true minimiser and that the rate of convergence of your iterations lies within the bounds calculated in part (a).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.1: Polynomial Functions Of Degree Greater Than
Problem 55E
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please help me with this question thanks guys

Let q(x) = x² Ax+b²x+c, where [1 0 1 1 0200 3 A = b = 10 30 1 100 4 Use Python or MATLAB for all parts of this question. (a) (2 points) Calculate the condition number of the matrix A and hence find an upper bound to the rate of convergence of the steepest descent method. (b) (5 points) Use the steepest descent method to find the minimiser, starting from x0 = (2,2,2,2). Tabulate the values of x that you find. Your table should have columns: k, xk, f(xk), uk, ||uk||, λk, and 1(x^-1(x*) f)xk-1-f(x*) (c) (2 points) Confirm that your algorithm does find the true minimiser and that the rate of convergence of your iterations lies within the bounds calculated in part (a).
Transcribed Image Text:Let q(x) = x² Ax+b²x+c, where [1 0 1 1 0200 3 A = b = 10 30 1 100 4 Use Python or MATLAB for all parts of this question. (a) (2 points) Calculate the condition number of the matrix A and hence find an upper bound to the rate of convergence of the steepest descent method. (b) (5 points) Use the steepest descent method to find the minimiser, starting from x0 = (2,2,2,2). Tabulate the values of x that you find. Your table should have columns: k, xk, f(xk), uk, ||uk||, λk, and 1(x^-1(x*) f)xk-1-f(x*) (c) (2 points) Confirm that your algorithm does find the true minimiser and that the rate of convergence of your iterations lies within the bounds calculated in part (a).
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