Answer the question below. (Linear Algebra and Numerical Method, Computer Science)
Problem 1 Background: In accordance with one of the basic design criteria employed in microwave power engineering, parameters of systems for microwave heating of dielectric materials should be adjusted to their dielectric properties. The designs of industrial devices for thermal processing of blocks of frozen meat were of limited success until the time when dielectric properties and other media parameters) of meat had been investigated at different temperatures. It turned out that the dielectric constant of different sorts of meat dramatically changes over the narrow temperature range around 0 C. While this experimental data is available in a tabulated format, some modern CAD tools (e.g., COMSOL Multiphysics) require representation of this data in a functional form. Data: The set of experimental values of the dielectric constant of raw beef as function of temperature was provided by P.O. Risman, Microtrans AB, Sweden, in 2000; they can be presented as follows: Temperature, -20 -15 -10 -5 -3 -2.2 -1.6 -1.3 10 20 35 50 65 80 Dielectric constant 4.9 5.5 6.1 12.3 22 30 42 46 48.9 49.2 48.9 48.2 46.9 45.5 43.6 41.7 -1.1 Questions Apply the method of Least Squares to the given data Visualize the experimental points along with the approximating functions, comment on the quality of approximation. Suggest a simple engineering solution significantly improving the initial approximation. Compose a MATLAB script implementing the entire solution: give an explicit analytical form of the obtained approximation Problem 1 Background: In accordance with one of the basic design criteria employed in microwave power engineering, parameters of systems for microwave heating of dielectric materials should be adjusted to their dielectric properties. The designs of industrial devices for thermal processing of blocks of frozen meat were of limited success until the time when dielectric properties and other media parameters) of meat had been investigated at different temperatures. It turned out that the dielectric constant of different sorts of meat dramatically changes over the narrow temperature range around 0 C. While this experimental data is available in a tabulated format, some modern CAD tools (e.g., COMSOL Multiphysics) require representation of this data in a functional form. Data: The set of experimental values of the dielectric constant of raw beef as function of temperature was provided by P.O. Risman, Microtrans AB, Sweden, in 2000; they can be presented as follows: Temperature, -20 -15 -10 -5 -3 -2.2 -1.6 -1.3 10 20 35 50 65 80 Dielectric constant 4.9 5.5 6.1 12.3 22 30 42 46 48.9 49.2 48.9 48.2 46.9 45.5 43.6 41.7 -1.1 Questions Apply the method of Least Squares to the given data Visualize the experimental points along with the approximating functions, comment on the quality of approximation. Suggest a simple engineering solution significantly improving the initial approximation. Compose a MATLAB script implementing the entire solution: give an explicit analytical form of the obtained approximation
