Solving the Linear Systems

Abstract

As has been seen in the preceding chapters, the numerical tracing of c(s) will generally involve the frequent calculation of both the tangent vectors and the execution of the corrector steps. This will require a sufficient amount of linear equation solving to warrant that it be done in an efficient and carefully considered manner. Here too, we shall treat the details of numerical linear algebra only in the context which concerns us viz. the calculation of tangent vectors t(A), and performing the operations w = A⁺b where A is an N × (N + 1) matrix with rank (A) = N which arise in the corrector steps. Readers interested in further background concerning numerical linear algebra may consult such textbooks on the subject as that of Golub & Van Loan.