Introduction to Numerical Analysis.

This well written book is enlarged by the following topics: $B$-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for the $LR$ and $QR$ algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations, preconditioning techniques and convergence rate of the conjugate gradient algorithm and multigrid methods for boundary value problems. Cf. also the reviews of the German original editions.