People employ the function-on-function regression to model the relationship between two random curves. Fitting this model, widely used strategies include algorithms falling into the framework of functional partial least squares (typically requiring iterative eigen-decomposition). Here we introduce a route of functional partial least squares based upon Krylov subspaces. It can be expressed in two forms equivalent to each other (in exact arithmetic): one is non-iterative with explicit forms of estimators and predictions, facilitating the theoretical derivation and potential extensions (to more complex models); the other one stabilizes numerical outputs. The consistence of estimators and predictions is established under regularity conditions. Our proposal is highlighted as it is less computationally involved. Meanwhile, it is competitive in terms of both estimation and prediction accuracy.

翻译：人们使用功能在功能上的回归来模拟两个随机曲线之间的关系。 适合这个模型, 广泛使用的战略包括可功能部分最小正方形框架的算法( 通常需要迭代 eigen 分解 ) 。 在这里, 我们引入了基于 Krylov 子空间的功能部分最小方形的路径。 它可以用两种等同的形式( 精确算术) 表达: 一种是不使用明确的估计和预测形式, 便于理论推断和潜在扩展( 更复杂的模型); 另一种是稳定数字输出。 估计和预测的一致性是在正常条件下建立的。 我们的建议在计算上不那么突出。 同时, 它在估算和预测准确性两方面都具有竞争力。