Reverse-time migration (Baysal et al., 1984) has some potential advantages with respect to downward-continuation migration. It can migrate overturned and prismatic reflections even in the presence of strong lateral velocity variations (Biondi, 2002). It also models the amplitude of the transmitted wavefield more accurately than downward-continuation in the presence of sharp interfaces. However,...

Explicit formulae for the inverse of an interval matrix of the form [I − ∆, I + ∆] (where I is the unit matrix) are proved via finding explicit solutions of certain nonlinear matrix equations.

The implicit midpoint rule (IMR) for nonexpansive mappings is established in Banach spaces. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a uniformly convex Banach space which either satisfies Opial’s property or has a Fréchet differentiable norm. Consequently, this algorithm applies in both `p and Lp for 1 < p < ∞.

where h >  is a stepsize. It is known that if f :RN →RN is Lipschitz continuous and sufficiently smooth, then the sequence {xn} generated by (.) converges to the exact solution of (.) as h→  uniformly over t ∈ [, t̄] for any fixed t̄ > . If we write the function f in the form f (t) = g(t) – t, then differential equation (.) becomes x′ = g(t)– t. Then the equilibrium problem associated w...

The present paper includes the local and semilocal convergence analysis of a fourth-order method based on quadrature formula in Banach spaces. weaker hypotheses used are only first Fréchet derivative. new approach provides residual errors, number iterations, radii, expected order convergence, estimates uniqueness solution. Such not provided approaches using Taylor expansions involving higher-or...