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A Singular Initial Value Problem to Construct Density-Equalizing Maps
| Content Provider | Semantic Scholar |
|---|---|
| Author | Andrés, Albert Avinyó Rubio, Juan De La Cruz De Solà-Morales I Guitart, Marta València I |
| Copyright Year | 2012 |
| Abstract | The diffusion-based algorithm to produce density-equalizing maps interprets diffusion as an advection process. This algorithm uses the dynamics of a flow that is defined by an initial value problem that turns out to be very singular at the initial time. The singularities appear when the initial density has line or angle discontinuities, which is always the case, for example, in area cartogram maps. This singular initial value problem is analyzed mathematically in this article and the conclusion is that despite these singularities, it has a unique solution. This justifies the extensive numerical use of this algorithm in the recent years. The techniques presented in this article use both partial and ordinary differential equations estimates. |
| Starting Page | 51 |
| Ending Page | 59 |
| Page Count | 9 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10884-011-9236-z |
| Volume Number | 24 |
| Alternate Webpage(s) | https://core.ac.uk/download/pdf/41767602.pdf |
| Alternate Webpage(s) | https://upcommons.upc.edu/bitstream/handle/2117/15276/preprint_martav.pdf;jsessionid=2C3190D73785BDA7AAA6058100892F85?sequence=1 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
