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Projection method
About: Projection method is a research topic. Over the lifetime, 3685 publications have been published within this topic receiving 85244 citations.
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TL;DR: In this paper, the authors review 30 years of developments and applications of the variable projection method for solving separable nonlinear least-squares problems and present a variety of applications from electrical engineering, medical and biological imaging, chemistry, robotics, vision, and environmental sciences.
Abstract: In this paper we review 30 years of developments and applications of the variable projection method for solving separable nonlinear least-squares problems. These are problems for which the model function is a linear combination of nonlinear functions. Taking advantage of this special structure, the method of variable projections eliminates the linear variables obtaining a somewhat more complicated function that involves only the nonlinear parameters. This procedure not only reduces the dimension of the parameter space but also results in a better-conditioned problem. The same optimization method applied to the original and reduced problems will always converge faster for the latter. We present first a historical account of the basic theoretical work and its various computer implementations, and then report on a variety of applications from electrical engineering, medical and biological imaging, chemistry, robotics, vision, and environmental sciences. An extensive bibliography is included. The method is particularly well suited for solving real and complex exponential model fitting problems, which are pervasive in their applications and are notoriously hard to solve.
752 citations
TL;DR: The main contributions of this work concern the formulation and the implementation of a multilevel self-adaptive version of the Immersed Boundary Method on locally refined meshes.
677 citations
TL;DR: This work couple the level set scheme to an adaptive projection method for the incompressible Navier?Stokes equations, in order to achieve higher resolution of the free surface with a minimum of additional expense.
651 citations
TL;DR: In this article, a general numerical approach, the projection method, is described to solve operator equations which arise in economic models. But this approach will involve error, and it is shown that the numerical approximations can be viewed as equilibria with boundedly rational agents.
630 citations
TL;DR: A new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion, achieving second-order temporal accuracy and better than first-order spatial accuracy in L"2-norms for one- and two-dimensional test problems.
626 citations