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12 Solving Algebraic Equations

Stan provides a built-in mechanism for specifying systems of algebraic equations. These systems can be solved either with the Newton method, as implemented in the Kinsol package (Hindmarsh et al. 2005), or with the Powell hybrid method (Powell 1970). The function signatures for Stan’s algebraic solvers are fully described in the algebraic solver section of the reference manual.

Solving any system of algebraic equations can be translated into a root-finding problem, that is, given a function \(f\), we wish to find \(y\) such that \(f(y) = 0\).


Hindmarsh, Alan C, Peter N Brown, Keith E Grant, Steven L Lee, Radu Serban, Dan E Shumaker, and Carol S Woodward. 2005. SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers.” ACM Transactions on Mathematical Software (TOMS) 31 (3): 363–96.
Powell, Michael J. D. 1970. “A Hybrid Method for Nonlinear Equations.” In Numerical Methods for Nonlinear Algebraic Equations, edited by P. Rabinowitz. Gordon; Breach.