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Read these instructions carefully: - You are required to upload a PDF report to Canvas along with a zip of your code. - The report should be a maximum of 3 pages long with references included. Minimum font size 10pts and margins of at least linch on A4 or standard letter size paper. - Do not include your code in the report. Simply create a zip file of your main scripts and functions, without figures or data sets included, and upload the zip file to Canvas. - Your report should be formatted as follows: - Title/author: Title of report, your name and email address. This is not meant to be a separate title page. - Sec. 1. Introduction and overview of the problem. - Sec. 2. Theoretical background and description of algorithms. - Sec. 3. Computational Results - Sec. 4. Summary and Conclusions - References - I suggest you use LTEX (Overleaf is a great option) to prepare your reports. A template is provided on Canvas under the Syllabus tab. You are also welcome to use Microsoft Word or any other software that properly typesets mathematical equations. - I encourage collaborations, however, everything that is handed in (both your report and your code) should be your work. - Your homework will be graded based on how completely you solved it as well as neatness and little things like: did you label your graphs and include figure captions. The homework is worth 10 points. 5 points will be given for the overall layout, correctness and neatness of the report, and 5 additional points will be for specific technical things and computational results that the TAs will look for in the report itself. WARM UP Look up the following functions and commands in Python: - Generating a uniform set of points in an interval: numpy.1inspace - Constructing Vandermonde matrices: numpy. vander - Solving matrix equations and computing determinants: numpy. linalg. solve, numpy.linalg. det - Trigonometric functions in numpy: numpy . sin and numpy. cos - Creating high quality plots with matplotlib. pyplot, labeling axes and legends, setting figure sizes and axis limits. Problem Deschiption Your goal in this HW is to interpolate Runge's function and investigate the numerical accuracy and stability of this problem. PART I 1. Consider the function f(x)=1+25x21,x[1,1]. and let x=(x0,,xN1)RN be a uniform grid of N points in the interval [1,1], i.e, xj=N12j1. Your goal is to find a polynomial Read these instructions carefully: - You are required to upload a PDF report to Canvas along with a zip of your code. - The report should be a maximum of 3 pages long with references included. Minimum font size 10pts and margins of at least linch on A4 or standard letter size paper. - Do not include your code in the report. Simply create a zip file of your main scripts and functions, without figures or data sets included, and upload the zip file to Canvas. - Your report should be formatted as follows: - Title/author: Title of report, your name and email address. This is not meant to be a separate title page. - Sec. 1. Introduction and overview of the problem. - Sec. 2. Theoretical background and description of algorithms. - Sec. 3. Computational Results - Sec. 4. Summary and Conclusions - References - I suggest you use LTEX (Overleaf is a great option) to prepare your reports. A template is provided on Canvas under the Syllabus tab. You are also welcome to use Microsoft Word or any other software that properly typesets mathematical equations. - I encourage collaborations, however, everything that is handed in (both your report and your code) should be your work. - Your homework will be graded based on how completely you solved it as well as neatness and little things like: did you label your graphs and include figure captions. The homework is worth 10 points. 5 points will be given for the overall layout, correctness and neatness of the report, and 5 additional points will be for specific technical things and computational results that the TAs will look for in the report itself. WARM UP Look up the following functions and commands in Python: - Generating a uniform set of points in an interval: numpy.1inspace - Constructing Vandermonde matrices: numpy. vander - Solving matrix equations and computing determinants: numpy. linalg. solve, numpy.linalg. det - Trigonometric functions in numpy: numpy . sin and numpy. cos - Creating high quality plots with matplotlib. pyplot, labeling axes and legends, setting figure sizes and axis limits. Problem Deschiption Your goal in this HW is to interpolate Runge's function and investigate the numerical accuracy and stability of this problem. PART I 1. Consider the function f(x)=1+25x21,x[1,1]. and let x=(x0,,xN1)RN be a uniform grid of N points in the interval [1,1], i.e, xj=N12j1. Your goal is to find a polynomial