residue function

Partial fraction expansion

Finds the residues, poles, and direct term of a Partial Fraction Expansion of the ratio of two polynomials.

residue(b, a, tol = 0.001)

rresidue(r, p, k, tol = 0.001)

Arguments

• b: coefficients of numerator polynomial
• a: coefficients of denominator polynomial
• tol: tolerance. Default: 0.001
• r: residues of partial fraction expansion
• p: poles of partial fraction expansion
• k: direct term

Returns

For residue, a list containing r, p and k. For rresidue, a list containing b and a.

Details

The call res <- residue(b, a) computes the partial fraction expansion for the quotient of the polynomials, b and a.

The call res <- rresidue(r, p, k) performs the inverse operation and computes the reconstituted quotient of polynomials, b(s) / a(s), from the partial fraction expansion; represented by the residues, poles, and a direct polynomial specified by r, p and k, and the pole multiplicity e.

Examples

b <- c(-4, 8)
a <- c(1, 6, 8)
rpk <- residue(b, a)
ba <- rresidue(rpk$r, rpk$p, rpk$k)

Author(s)

Tony Richardson, arichard@stark.cc.oh.us ,

Ben Abbott, bpabbott@mac.com ,

adapted by John W. Eaton.

Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com