MATLAB数值计算功能详解：多项式的表达与创建Chapter 4

Chapter 4 of MATLAB: Numerical Computation introduces the various functions and capabilities of MATLAB for performing numerical computations, with a focus on polynomials. Polynomials are commonly used in mathematical modeling and analysis. In MATLAB, polynomials are expressed using a row vector of coefficients, where each element corresponds to a term in descending order of variables. For example, a polynomial P(x) = a0xn + a1xn-1 + a2xn-2 + ... + an-1x + an can be represented as a vector of coefficients P = [a0 a1 ... an-1 an]. The roots of a polynomial can also be represented as a vector, and the relationship between the coefficient vector and the root vector can be expressed as the product of (x - ar1)(x - ar2) ... (x - arn) = a0xn + a1xn-1 + a2xn-2 + ... + an-1x + an. To create polynomials in MATLAB, the poly2sym function can be used to input the coefficient vector directly, making it easy to establish symbolic representations. In addition, MATLAB provides a range of functions for working with polynomials, such as evaluating polynomials, finding roots, factorizing, and performing arithmetic operations. Polynomial interpolation is another important aspect of numerical computation in MATLAB. The polyfit function can be used to fit a polynomial to a set of data points, while the polyval function can then be used to evaluate the polynomial at specific points. This allows for the approximation of functions based on limited data, which is essential for many engineering and scientific applications. Overall, MATLAB's numerical computation capabilities make it a powerful tool for analyzing and solving problems involving polynomials. By utilizing the functions and methods outlined in Chapter 4, users can efficiently work with polynomials and perform a wide range of numerical computations with ease and accuracy.