WCpqr79 WCpqr792 WCpzero WCpzero2 WDka WDka2 WRpzero WRpzero2

WDka() Function WDka ( N As  Long, A As  Variant  ) Roots of a polynomial (complex coefficients) DKA method (complex number representation in Excel format) Purpose WDka computes all roots of a polynomial p(z) with complex coefficients by DKA (Durand-Kerner-Aberth) method. p(z) = a0*z^n + a1*z^(n-1) + ... + an To represent complex numbers in Excel cells, complex number format in Excel (e.g. 2.5+1i) is used. Worksheet function Complex can be used to input complex numbers into cells. Returns N+2 x 1 Column 1 Rows 1 to N Roots Row N+1 Return code Row N+2 Number of iterations performed to converge Return code. = 0: Successful exit. = 1: Maximum number of iterations exceeded. Parameters [in] N Degree of polynomial. (N >= 1) [in] A (N+1 x 1) or (1 x N+1) Complex coefficients a0 to an of polynomial a0 x^n + a1 x^(n-1) + … + a(n-1)x + an. Reference (Japanese book) Masatake Mori "FORTRAN77 Numerical Calculation Programming (augmented edition)" Iwanami Shoten (1987) Example Solve the following algebraic equation. x^3 + (-19-14i)*x^2 + (67+191i)*x + 116-612i = 0 The exact solutions are 8 + 4i, 4 + 9i and 7 + i.