TY - JOUR TI - Collocation methods for some singular integral equations in linear transport theory AU - Kelley, C.T. AU - Mullikin, T.W. T2 - Journal of Integral Equations DA - 1982/// PY - 1982/// VL - 4 SP - 77–88 ER - TY - JOUR TI - Approximation of solutions to some quadratic integral equations in transport theory AU - Kelley, C.T. T2 - Journal of Integral Equations DA - 1982/// PY - 1982/// VL - 4 SP - 221–237 ER - TY - JOUR TI - Convergence Acceleration for Newton’s Method at Singular Points AU - Decker, D. W. AU - Kelley, C. T. T2 - SIAM Journal on Numerical Analysis AB - If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, linear convergence of the Newton sequence to the root is the best that one can expect. In this paper we give sufficient conditions under which Newton’s method may be modified to produce a sequence $\{ x_n \} $ such that the subsequence $\{ x_{2n} \} $ converges quadratically to the root. DA - 1982/2// PY - 1982/2// DO - 10.1137/0719012 VL - 19 IS - 1 SP - 219-229 J2 - SIAM J. Numer. Anal. LA - en OP - SN - 0036-1429 1095-7170 UR - http://dx.doi.org/10.1137/0719012 DB - Crossref ER - TY - JOUR TI - Approximate methods for the solution of the Chandrasekhar H‐equation AU - Kelley, C. T. T2 - Journal of Mathematical Physics AB - We consider two methods of approximate solution to matrix valued analogs of the Chandrasekhar H-equation. We give conditions under which they converge. The first method is a generalization of approximation of the integral by a quadrature. The second is Newton’s method. DA - 1982/11// PY - 1982/11// DO - 10.1063/1.525251 VL - 23 IS - 11 SP - 2097-2100 J2 - Journal of Mathematical Physics LA - en OP - SN - 0022-2488 1089-7658 UR - http://dx.doi.org/10.1063/1.525251 DB - Crossref ER -