# The two examples in the paper "Nearest singular polynomial." ## Example 1: f1:=evalf(x^5-x); N_m_1_2:=0.1763296120; N_m_1_3:=0.6261127476; ## Example 2: f2:=expand((x-0.89-0.03*I)*(x-0.88+0.02*I)*(x-0.87)*(x-1)); N_m_2_2:=1.55738888907*10^(-13); N_m_2_3:=9.817251548*10^(-10); N_m_2_4:=1.958555857*10^(-5); ## The examples in the paper " Hybird method for computing Nearest Singular Polynomials". ## Example 3: f3:=x^4-0.960000*x^3-0.0401*x^2+0.000096*x+0.000004; N_m_3_2:=1.645038*10^(-11); N_m_3_3:=4.144531*10^(-7); N_m_3_4:=0.104999; ## Example 4: f4:=x^5+2.03*x^4-0.9398*x^3-2.0296*x^2-0.0602*x-0.0004; N_m_4_2:=2.460988*10^(-9); N_m_4_3:=0.368179; ## Example 5: f5:=x^6+1.99*x^5-9.0202*x^4-1.9104*x^3+8.0218*x^2-0.0796*x-0.0016; N_m_5_2:=3.231668*10^(-6); N_m_5_3:=5.766062; #Example 6: f6:=x^6+2.04*x^5-0.9199*x^4-2.039806*x^3-0.080112*x^2-0.000194*x+0.000012; N_m_6_2:=3.009789*10^(-12); N_m_6_3:=7.453849*10^(-7); N_m_6_4:=0.444902; ## Example 7: f7:=x^5+(0.909091+0.1*I)*x^4-10*x^3-(9.09091-I)*x^2+9.0*x+8.181818+0.9*I; N_m_7_2:=0.0123884; ## Example 8: f8:=x^21-1.142857*x^20-1.0*x^19+2.714286*x^18-4.0*x^17+4.1428714*x^16-2.571371*x^15+x^14+0.857143*x^13 -3.142857*x^12+2.0*x^11+0.285714*x^10+0.571428*x^8-1.285600*x^7+2.857143*x^6-4.714286*x^5+2.142857*x^4 +0.428571*x^3+0.857143*x^2-0.714286*x-0.285700; N_m_8_2:=0.190477*10^(-8); N_m_8_3:=0.0000963776;