The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B. A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography. The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level.
In Section 2 we will deal with the “discrete” case. Let S be a locally finite tree T endowed with the natural integer-valued distance function: the ...
... for in this case [yp](s)=s[yp](s), [yp](s)=s2[yp](s). As we will see in the examples, this assumption also makes it possible to deal with the initial ...
x,y∈S δ(x,y) is maximum. u(x) + ADDITIVE SUBSET CHOICE Input: A set X = {x1 ,x2 ... F Tractability cycle Test 8.2 How (Not) to Deal with Intractability 173.
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... partial differential equations have received a great deal of attention. For excellent bibliographical coverage, see Todd (1956), Richtmyer (1957), ...
Todd, P. A., McKeen, .l. ... ANALYTICAL SUPPORT PROBLEM SOLVING Cognitive Perspectives on Modelling HOW DO STUDENTS AND TEACHERS DEAL Sodhi and Son 219 NOTE ...