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The design and optimization of the high-speed digital subscriber line (HDSL) need powerful computational strategies. Traditional techniques of distributing poles and zeros on Smith charts generally do not work. In the past, such approaches have lead to suboptimal designs for applications where the data capacity sought is considerably less than the Shannon capacity of the lines. Typical subscriber loops are less than perfect and for the current demands on the HDSL at T1/T2 and El rates every possible venue for the HDSL design needs to be investigated, if not exploited. In this Chapter, flexible computational techniques are presented that explore and optimize system components in view of the operating environment of the HDSL and/or the asymmetric digital subscriber line (ADSL) and inherent limitations of system components. The optimization occurs automatically by forcing the computer to track the effects of incremental changes of the subsystem performance (e.g., echo cancelers or equalizers), or the component values (Rs and Cs in the matching circuits) in context to the functional constraints of the (HDSL, ADSL, duplex, dual-duplex, triplex, etc.) line in conjunction with various subscriber loop environments (CSA loops, loops d2c66b5586