FindRoot
Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand. No examples yet — the crosswalk is the reason it has a page.
FindRoot(equations, params): numerically find parameter values that zero the residuals. equations is an equation (lhs == rhs), a bare residual expression (read as = 0), or a list of either. params is a list of specs (a bare symbol, (a, a0), or (a, a0, lo, hi) with box constraints), matching FindFit. Returns a record {parameters, converged, stationary, residualNorm, iterations}. converged is true only at a root: every residual is within the engine's tolerance scaled by its own equation, |r_i| ≤ tolerance · (1 + Σ_j |J_ij| · max(1, |θ_j|)), with J the Jacobian and θ the parameters, so a minimum of the sum of squared residuals that is not a root (a^2 + 1 = 0) is converged: False. When the residual is above tolerance, the residual itself must confirm the Jacobian term: with each parameter moved by ±2 · tolerance · max(1, |θ_j|) toward and away from the zero, the change of the residual is the change the Jacobian predicts to within half, and the residual reaches tolerance, changes sign, or touches 0 to within the rounding of the parameters. So a steep equation with no root (2 - sin(10^18 a) = 0) is not converged either. stationary is the solver's own stop test, true at such a minimum too; a stacked system of data rows next to an equation reads it as FindFit reads converged. An optional third argument is the options dictionary of FindFit: {global: {b: [lo, hi]}} searches the named parameters (at most two) over the range for the lowest sum of squared residuals of the whole system; the constant phase coefficients of the equations (3.22 in cos(3.22 b + c)) space the grid as the span of a variable does for a fit. With a kernel pool on the engine (ce.workers), evaluateAsync() scans the grid on the workers.
FindRoot(any, any, dictionary?) -> dictionaryas compute-engine declares itTyped signatures
| Type | Package | Applies |
|---|---|---|
(any, any, dictionary?) -> dictionary | compute-engine | always |