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67 lines
1.6 KiB
Markdown
67 lines
1.6 KiB
Markdown
# Homotopy Continuation in Julia
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This is a project for the "Laboratorio Computazionale" exam at the University of Pisa
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## Implemented
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- Total-degree Homotopy with "Roots of unity" start system
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- Euler-Newton predictor-corrector method with adaptive step size
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- Homotopy Continuation for all roots of the target system
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## TODO
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- [x] Parallelization
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- ~~Homogenization~~
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## Example systems
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Here's some tests on 2x2 systems, with the plotted real approximate solutions
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$$
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\begin{align*}
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x^3 + 5x^2 - y - 10 &= 0 \\
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2x^2 - y - 10 &= 0 \\
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\end{align*}
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$$
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| Single-threaded | Multi-threaded (nproc=6) |
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|-------------------|---------------------------------|
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---
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$$
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\begin{align*}
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x^2 + 2y &= 0 \\
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y - 3x^3 &= 0 \\
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\end{align*}
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$$
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| Single-threaded | Multi-threaded (nproc=6) |
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|-------------------|---------------------------------|
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$$
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\begin{align*}
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x^2 + y^2 - 4 &= 0 \\
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xy - 1 &= 0 \\
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\end{align*}
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$$
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| Single-threaded | Multi-threaded (nproc=6) |
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|-------------------|---------------------------------|
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---
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$$
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\begin{align*}
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x^2 + y^2 - 2 &= 0 \\
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xy - 1 &= 0 \\
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\end{align*}
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$$
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| Single-threaded | Multi-threaded (nproc=6) |
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|-------------------|---------------------------------|
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