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This first title in SIAM's Spotlights book series is about the
interplay between modeling, analysis, discretization, matrix
computation, and model reduction. The authors link PDE analysis,
functional analysis, and calculus of variations with matrix
iterative computation using Krylov subspace methods and address the
challenges that arise during formulation of the mathematical model
through to efficient numerical solution of the algebraic problem.
The book's central concept, preconditioning of the conjugate
gradient method, is traditionally developed algebraically using the
preconditioned finite-dimensional algebraic system. In this text,
however, preconditioning is connected to the PDE analysis, and the
infinite-dimensional formulation of the conjugate gradient method
and its discretization and preconditioning are linked together.
This text challenges commonly held views, addresses widespread
misunderstandings, and formulates thought-provoking open questions
for further research.
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