Partial fractions in the PLA only from the denominator polynomial

This chapter deals with partial fractions in the PLA only from the denominator polynomial. The PLA offers an analytical expression for the residue d_k with no recourse to the total eigenvector at all. Since the eigenvalues {uk}k=1K are the same in both the Lanczos formalism and in the PLA, the corresponding residues {d_k} must also coincide with each other. The special inverse proportionality between P_K:(u_k) and QK-1-1(uk) is valid only at the eigenvalues u = u_k.