- Referenced in 129 articles
- iterative (preconditioned Krylov) methods instead of direct methods for these linear systems. The most recent...
- Referenced in 109 articles
- systems that arise are solved by direct methods (LU factor/solve). LSODE supersedes the older GEAR...
- Referenced in 146 articles
- Convergence properties of the Nelder--Mead simplex method in low dimensions The Nelder--Mead simplex ... enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially...
- Referenced in 90 articles
- Interface Calculation). SLIC is an alternating-direction method for the geometric approximation of fluid interfaces ... space dimensional components, one for each coordinate direction. (2) These onedimensional components are composed entirely ... right in the coordinate direction under consideration. (4) Because of the completely one-dimensional nature ... possible to incorporate any one space dimensional method for advancing contact discontinuities. This makes SLIC...
- Referenced in 390 articles
- path-following method, with either the HKM or the NT search direction. The basic code ... semideﬁnite cones are calculated via the Lanczos method. Numerical experiments show that this general purpose...
- Referenced in 99 articles
- exploited to define a modified Newton method which can be applied to problems that ... possible to compute a negative-curvature direction at a stationary point. The above mentioned modified ... preconditioned truncated Newton method is described that defines a search direction which interpolates between ... nonlinear conjugate-gradient-type method and a modified Newton direction. Numerical results are given which...
- Referenced in 493 articles
- author and his group. Implicit filtering methods use finite difference approximations of the gradient, which ... noise level in the function. Direct search algorithms, including the Nelder-Mead, multidirectional search ... conclude with a numerical demonstration of the methods discussed in the respective chapter, and with...
- Referenced in 49 articles
- basic optimization algorithm is the Method of Feasible Directions. The user must provide a main ... also be solved, and the conjugate direction method of Fletcher and Reeves is used...
- Referenced in 48 articles
- sparse. The current release features direct methods based on Gaussian elimination without pivoting...
- Referenced in 47 articles
- those of grid-independent convergence of multigrid methods. The multi-level algorithms implemented by BILUM ... enough to be solved by a direct method or a preconditioned iterative method...
- Referenced in 98 articles
- Volume-of-fluid (VOF) methods are popular for the direct numerical simulation of time-dependent ... multiple liquids. As in any numerical method, however, it has its weaknesses, namely, for flows...
- Referenced in 36 articles
- practical steps involved in implementing the methods, culminating in readers learning how to write programs ... book begins with a review of direct methods for the solution of linear systems, with...
- Referenced in 84 articles
- range of automated proof methods. Interactive proof development is supported directly as well. The Isabelle...
- Referenced in 71 articles
- efficacy of the method. Finally, we indicate the current directions of the research...
- Referenced in 27 articles
- variables (some hundred at most). An SLP method with estimation of gradients by linear interpolation ... only. M. Powell’s paper on Direct Search Methods...
- Referenced in 87 articles
- conjugate gradient method with an incomplete Cholesky factorization to generate a direction, and a projected...
- Referenced in 34 articles
- arising in the direct sparse PCA method...
- Referenced in 84 articles
- class of methods consists of techniques derived from modifications of a given direct solver...
- Referenced in 94 articles
- methods employed by the theory of dynamical systems allow to compute important properties directly without...
- Referenced in 11 articles
- million equations) ever solved by a direct method, with the highest performance (51 GFLOPS...