Answer: experimental data fitting method: the experimental data are often a set of discrete sequences, which contain inevitable errors, or cannot satisfy a certain function at the same time, then we use the approximation function ψ(x) to optimally approximate the sample points. This method is called fitting function.

Model parameter fitting method: in a reaction engineering experiment, different models are used to fit the experimental data for a group of measured data, and the best model and simulation parameters are obtained.

Examples: linear fitting function, quadratic fitting function.

(2) Similarities and differences between linear fitting and quadratic fitting functions.

Linear fitting: given a set of data (xi, Yi), I = 1, 2 ..., m is the fitting straight line P (x) = A0+a1x;

Quadratic fitting: given the data arrangement (,easy), I = 1, 2 ..., m, use quadratic polynomial function p(x)=a0+a 1x+a2x2 to fit each group of data.

Similarities: Both of them are approximation functions based on the principle of minimum errors of Q and Y, both of them are used to fit discrete function groups, and both of them are used to fit univariate functions.

Difference: the function constructed by linear fitting is quadratic, and the function constructed by quadratic fitting is quadratic.

(3) What is the contradictory equation and how to solve it?

A: In general, when the number of equations n is greater than the number of variables m, and there is no linear correlation between m equations, the equation has no solution. At this time, the equation is called a contradiction equation. In general, the equations have no solution, that is, it is impossible to find n variables to satisfy m equations at the same time. This situation and the fitting curve can't satisfy all the experimental data points at the same time, so we can solve the mean square error min || ax-y) ||| 22? In the smallest sense, the solutions of contradictory equations are exchanged for fitting curves. It can also be proved by mathematical knowledge that the solution of the equation set ATAX=ATY is the solution of the contradictory equation set AX=Y under the least square method.

(4) What is the solution of the nonlinear equation? Try to say more than five ways.

Answer: For the general nonlinear equation f(x)=0, there are usually multiple roots, so it is impossible to determine the method to solve the month, but only one root can be found by any method. Therefore, when solving nonlinear equations, the range of initial values or solutions should be given. Solving the roots of the equation f(x)=0 by corresponding methods is called nonlinear equation solving.

Methods: Dichotomy, direct iteration, relaxation iteration, Newton iteration and secant method.