Back in time. fast. Accelerated time iterations
提出两种互补算法（加速时间迭代法和牛顿-克雷洛夫求解器）来求解非线性理性预期模型，通过显式构造导数算子实现二次收敛，大幅缩短计算时间，适用于消费储蓄、真实经济周期和两国模型等基准模型。
We present two complementary algorithms to solve nonlinear rational expectations models characterized by first order conditions: an accelerated time-iteration method and a Newton–Krylov solver. Both approaches exploit an explicit construction of the derivative operator (and the model Jacobian) and achieve quadratic convergence near the solution, yielding large computational gains over standard time iteration. We show how to apply these linear operators without forming dense matrices and invert the resulting systems efficiently using truncated Neumann series or GMRES. On three benchmark models (consumption–savings, RBC, and a two-country model), the two methods produce the same solution with substantially reduced runtimes.