Displaying similar documents to “Reconstruction of map projection, its inverse and re-projection”

On melancholic magic squares

Götz Trenkler, Dietrich Trenkler (2013)

Discussiones Mathematicae Probability and Statistics

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Starting with Dürer's magic square which appears in the well-known copper plate engraving Melencolia we consider the class of melancholic magic squares. Each member of this class exhibits the same 86 patterns of Dürer's magic square and is magic again. Special attention is paid to the eigenstructure of melancholic magic squares, their group inverse and their Moore-Penrose inverse. It is seen how the patterns of the original Dürer square to a large extent are passed down also to the inverses...

Explicit solutions of infinite linear systems associated with group inverse endomorphisms

Fernando Pablos Romo (2022)

Czechoslovak Mathematical Journal

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The aim of this note is to offer an algorithm for studying solutions of infinite linear systems associated with group inverse endomorphisms. As particular results, we provide different properties of the group inverse and we characterize EP endomorphisms of arbitrary vector spaces from the coincidence of the group inverse and the Moore-Penrose inverse.

Complexity of Partial Inverse Assignment Problem and Partial Inverse Cut Problem

Xiaoguang Yang (2010)

RAIRO - Operations Research

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For a given partial solution, the partial inverse problem is to modify the coefficients such that there is a full solution containing the partial solution, while the full solution becomes optimal under new coefficients, and the total modification is minimum. In this paper, we show that the partial inverse assignment problem and the partial inverse minimum cut problem are NP-hard if there are bound constraints on the changes of coefficients.

On inversions of van der Grinten projections

Tomáš Bayer, Milada Kočandrlová (2021)

Applications of Mathematics

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Approximately 150 map projections are known, but the inverse forms have been published for only two-thirds of them. This paper focuses on finding the inverse forms of van der Grinten projections I--IV, both by non-linear partial differential equations and by the straightforward inverse of their projection equations. Taking into account the particular cases, new derivations of coordinate functions are also presented. Both the direct and inverse equations have the analytic form, are easy...