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We propose a unified framework for a broad class of methods to solve projected equations that approximate the solution of a high-dimensional fixed point problem within a subspace S spanned by a small number of basis functions or features. These methods originated in approximate dynamic programming (DP), where they are collectively known as temporal difference (TD) methods. Our framework is based on a connection with projection methods for monotone variational inequalities, which involve alternative representations of the subspace S (feature scaling). Our methods admit simulation-based implementations, and even when specialized to DP problems, include extensions/new versions of the standard TD algorithms, which offer some special implementation advantages and reduced overhead.