Computational Mathematics
Homotopy methods are a set of mathematical techniques used to solve nonlinear equations by continuously transforming a simple problem into a more complex one while maintaining the solutions throughout the transformation. This approach is particularly useful in nonlinear programming, where finding solutions can be challenging due to the nature of the equations involved. Homotopy methods rely on the concept of deforming a known solution to a simpler problem into the solution of a more complicated problem, allowing for the exploration of solution paths and stability.
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