steepest-descent paths
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6 matching pages
1: 5.21 Methods of Computation
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►Another approach is to apply numerical quadrature (§3.5) to the integral (5.9.2), using paths of steepest descent for the contour.
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2: 3.5 Quadrature
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§3.5(ix) Other Contour Integrals
… ►For example, steepest descent paths can be used; see §2.4(iv). … ►The steepest descent path is given by , or in polar coordinates we have . … ►A special case is the rule for Hilbert transforms (§1.14(v)): …3: 9.17 Methods of Computation
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►In the first method the integration path for the contour integral (9.5.4) is deformed to coincide with paths of steepest descent (§2.4(iv)).
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4: Bibliography T
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Steepest descent paths for integrals defining the modified Bessel functions of imaginary order.
Methods Appl. Anal. 1 (1), pp. 14–24.
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5: 36.5 Stokes Sets
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►where denotes a real critical point (36.4.1) or (36.4.2), and denotes a critical point with complex or , connected with by a steepest-descent path (that is, a path where ) in complex or space.
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6: 2.4 Contour Integrals
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►Paths on which is constant are also the ones on which decreases most rapidly.
…However, for the purpose of simply deriving the asymptotic expansions the use of steepest descent paths is not essential.
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