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This book is intended to help advanced undergraduate, graduate, and
postdoctoral students in their daily work by offering them a
compendium of numerical methods. The choice of methods pays
significant attention to error estimates, stability and convergence
issues, as well as optimization of program execution speeds.
Numerous examples are given throughout the chapters, followed by
comprehensive end-of-chapter problems with a more pronounced
physics background, while less stress is given to the explanation
of individual algorithms. The readers are encouraged to develop a
certain amount of skepticism and scrutiny instead of blindly
following readily available commercial tools. The second edition
has been enriched by a chapter on inverse problems dealing with the
solution of integral equations, inverse Sturm-Liouville problems,
as well as retrospective and recovery problems for partial
differential equations. The revised text now includes an
introduction to sparse matrix methods, the solution of matrix
equations, and pseudospectra of matrices; it discusses the sparse
Fourier, non-uniform Fourier and discrete wavelet transformations,
the basics of non-linear regression and the Kolmogorov-Smirnov
test; it demonstrates the key concepts in solving stiff
differential equations and the asymptotics of Sturm-Liouville
eigenvalues and eigenfunctions. Among other updates, it also
presents the techniques of state-space reconstruction, methods to
calculate the matrix exponential, generate random permutations and
compute stable derivatives.
This book helps advanced undergraduate, graduate and postdoctoral
students in their daily work by offering them a compendium of
numerical methods. The choice of methods pays significant attention
to error estimates, stability and convergence issues as well as to
the ways to optimize program execution speeds. Many examples are
given throughout the chapters, and each chapter is followed by at
least a handful of more comprehensive problems which may be dealt
with, for example, on a weekly basis in a one- or two-semester
course. In these end-of-chapter problems the physics background is
pronounced, and the main text preceding them is intended as an
introduction or as a later reference. Less stress is given to the
explanation of individual algorithms. It is tried to induce in the
reader an own independent thinking and a certain amount of
scepticism and scrutiny instead of blindly following readily
available commercial tools.
This book is intended to help advanced undergraduate, graduate, and
postdoctoral students in their daily work by offering them a
compendium of numerical methods. The choice of methods pays
significant attention to error estimates, stability and convergence
issues, as well as optimization of program execution speeds.
Numerous examples are given throughout the chapters, followed by
comprehensive end-of-chapter problems with a more pronounced
physics background, while less stress is given to the explanation
of individual algorithms. The readers are encouraged to develop a
certain amount of skepticism and scrutiny instead of blindly
following readily available commercial tools. The second edition
has been enriched by a chapter on inverse problems dealing with the
solution of integral equations, inverse Sturm-Liouville problems,
as well as retrospective and recovery problems for partial
differential equations. The revised text now includes an
introduction to sparse matrix methods, the solution of matrix
equations, and pseudospectra of matrices; it discusses the sparse
Fourier, non-uniform Fourier and discrete wavelet transformations,
the basics of non-linear regression and the Kolmogorov-Smirnov
test; it demonstrates the key concepts in solving stiff
differential equations and the asymptotics of Sturm-Liouville
eigenvalues and eigenfunctions. Among other updates, it also
presents the techniques of state-space reconstruction, methods to
calculate the matrix exponential, generate random permutations and
compute stable derivatives.
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