Page 209. Frobenius Decomposition of Positive Compact Operators R. Jang and HD Victory, Jr. ... T... more Page 209. Frobenius Decomposition of Positive Compact Operators R. Jang and HD Victory, Jr. ... The most general results on Page 210. 196 Jang and Victory (B) are due, however, to F. Niiro and I. Sawashima [21], HP Lotz [16], and HP Lotz and HH Schaefer [17]. ...
Numerical Functional Analysis and Optimization, 1982
Functional analytic methods, employing the CollectiVely compact operator approximation theory of ... more Functional analytic methods, employing the CollectiVely compact operator approximation theory of P.M. Anselone, are utilized to study the convergence properties of four improvements to the rather promising quadratic method of Gopinath, Natarajan, and Sundararaman [Nucl. Sci. Eng. 75 (1980), 181-184] for effecting slab transport calculations. This method displays a global discretization error of order four; our alterations too possess global
International Journal of Computer Mathematics, 1983
A method of order three for finding multiple zeros of nonlinear functions is developed. The metho... more A method of order three for finding multiple zeros of nonlinear functions is developed. The method requires two evaluations of the function and one evaluation of the derivative per step.
A procedure to accelerate the convergence of quasi-Monte Carlo approximations is described and in... more A procedure to accelerate the convergence of quasi-Monte Carlo approximations is described and investigated. The procedure applies a weighted least-squares smoothing method to improve the approximations that were obtained using low-discrepancy sequences. The acceleration procedure is tested computationally on several numerical integration problems including two problems of interest in mathematical finance. The results indicate that when Halton low-discrepancy points are used in the quasi-Monte Carlo method, the accelerated sequence often converges a factor of five or more faster than the original quasi-Monte Carlo approximations.
Page 209. Frobenius Decomposition of Positive Compact Operators R. Jang and HD Victory, Jr. ... T... more Page 209. Frobenius Decomposition of Positive Compact Operators R. Jang and HD Victory, Jr. ... The most general results on Page 210. 196 Jang and Victory (B) are due, however, to F. Niiro and I. Sawashima [21], HP Lotz [16], and HP Lotz and HH Schaefer [17]. ...
Numerical Functional Analysis and Optimization, 1982
Functional analytic methods, employing the CollectiVely compact operator approximation theory of ... more Functional analytic methods, employing the CollectiVely compact operator approximation theory of P.M. Anselone, are utilized to study the convergence properties of four improvements to the rather promising quadratic method of Gopinath, Natarajan, and Sundararaman [Nucl. Sci. Eng. 75 (1980), 181-184] for effecting slab transport calculations. This method displays a global discretization error of order four; our alterations too possess global
International Journal of Computer Mathematics, 1983
A method of order three for finding multiple zeros of nonlinear functions is developed. The metho... more A method of order three for finding multiple zeros of nonlinear functions is developed. The method requires two evaluations of the function and one evaluation of the derivative per step.
A procedure to accelerate the convergence of quasi-Monte Carlo approximations is described and in... more A procedure to accelerate the convergence of quasi-Monte Carlo approximations is described and investigated. The procedure applies a weighted least-squares smoothing method to improve the approximations that were obtained using low-discrepancy sequences. The acceleration procedure is tested computationally on several numerical integration problems including two problems of interest in mathematical finance. The results indicate that when Halton low-discrepancy points are used in the quasi-Monte Carlo method, the accelerated sequence often converges a factor of five or more faster than the original quasi-Monte Carlo approximations.
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