MATLAB Lecture 6 School of Mathematical Sciences Xiamen University http∥gdjpkc.xmu.edu.cr MATLAB Lecture 6-Polynomial 多项式 Ref: MATLAB-Mathematics-Polynomials and Interpolation Vocabulary: polynomial多项式 root根 arithmetic operation算术运算 multiply乘法 divide除法 derivative导数 differentiation微分法 求值 action 部分分式 展开 convolution卷积 product乘积 deconvolution去卷积 quotient商 remainder余项 multiple roots重根 direct直接的 term transfer function转换函数,传递函数 ● Some functions conv decon poly polyder polyval polyvalm roots *residue polyfit Y Representing Poly nomials MATLAB represents polynomials as row vectors containing coefficients ordered descending powers >>p=[10-2-5] %represents x'-2x-5 >> sym p= poly 2sym(p) represents a polynomial in sym form sym p- X^3-2*x-5 ☆ Create polynomials >>p=[10-2-5 % represents a polynomail x'-2x-5 0 >>r=[0, 1, -1]; poly(r) %generate a polynomial x(x-D(x+1), whose roots are 0, 1,-1 >>a=[12: 3 4; poly(a) generate the characteristic polynomials of matrix Lec6-IMATLAB Lecture 6  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Lec6­1 MATLAB Lecture 6 – Polynomial  多项式 Ref: MATLAB→Mathematics→Polynomials  and  Interpolation  l Vocabulary: polynomial  多项式 root  根 arithmetic operation  算术运算 multiply  乘法 divide 除法 derivative 导数 differentiation  微分法 evaluation  求值 partial­fraction  部分分式 expansion  展开 convolution  卷积 product  乘积 deconvolution  去卷积 quotient  商 remainder 余项 multiple roots 重根 direct  直接的 term  项 transfer function  转换函数，传递函数 l Some functions conv  deconv  poly  polyder polyval  polyvalm roots * residue * polyfit l Polynomials  ² Representing Polynomials MATLAB represents polynomials as  row  vectors  containing  coefficients ordered by  descending powers.  >> p = [1 0 ­2 ­5];  % represents 3 x - 2x -5 p =  1  0  ­2  ­5  >> sym_p = poly2sym(p) % represents a polynomial in sym form  sym_p =  x^3­2*x­5  ² Create Polynomials >> p = [1 0 ­2 ­5] % represents a polynomail 3 x - 2x -5 p =  1  0  ­2  ­5  >> r = [0, 1, ­1]; poly(r) %generate a polynomial  x(x -1)(x +1) ,whose roots are 0,1,­1  ans =  1  0  ­1  0  >> a = [1 2; 3 4]; poly(a) % generate the characteristic polynomials of matrix…  1 2  3 4 l l Ê - - ˆ Á ˜ Ë - - ¯ , i.e.  2  1 2  5 2  3 4 l l l l - - = - - - -