Solving the Monge–Ampère equations for the inverse reflector problem
نویسندگان
چکیده
منابع مشابه
the algorithm for solving the inverse numerical range problem
برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولSolving the Monge-Ampère Equations for the Inverse Reflector Problem
The inverse reflector problem arises in geometrical nonimaging optics: Given a light source and a target, the question is how to design a reflecting free-form surface such that a desired light density distribution is generated on the target, e.g., a projected image on a screen. This optical problem can mathematically be understood as a problem of optimal transport and equivalently be expressed ...
متن کاملAnalytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations
In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...
متن کاملSolving the Inverse Representation Problem
In this paper, we present an approach to extract most relevant information from a (semi-)quantitative knowledge base, e.g., from a probability distribution. Relevance here is meant with respect to some appropriate inductive inference process, like maximum entropy inference (ME-inference) in probabilistics. So in particular, the method developed in this paper is apt to solve the inverse maxent p...
متن کاملThe Reflector Problem and the Inverse-square Law
∗ We introduce a model to design reflectors that take into account the inverse-square law for radiation, i.e. it considers how far the reflector is from the source. The radiant intensity at the source and the irradiance distribution at the target are given. We prove the existence of solutions in the near field case, when the input and output energies are prescribed. A uniqueness property will a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Models and Methods in Applied Sciences
سال: 2015
ISSN: 0218-2025,1793-6314
DOI: 10.1142/s0218202515500190