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Lattice Methods for Multiple Integration (Hardcover)
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Lattice Methods for Multiple Integration (Hardcover)
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This is the first book devoted to lattice methods, a recently
developed way of calculating multiple integrals in many variables.
Multiple integrals of this kind arise in fields such as quantum
physics and chemistry, statistical mechanics, Bayesian statistics
and many others. Lattice methods are an effective tool when the
number of integrals are large. The book begins with a review of
existing methods before presenting lattice theory in a thorough,
self-contained manner, with numerous illustrations and examples.
Group and number theory are included, but the treatment is such
that no prior knowledge is needed. Not only the theory but the
practical implementation of lattice methods is covered. An
algorithm is presented alongside tables not available elsewhere,
which together allow the practical evaluation of multiple integrals
in many variables. Most importantly, the algorithm produces an
error estimate in a very efficient manner. The book also provides a
fast track for readers wanting to move rapidly to using lattice
methods in practical calculations. It concludes with extensive
numerical tests which compare lattice methods with other methods,
such as the Monte Carlo.
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