Introduction to Numerical Analysis
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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.