Steve Ellington N4LQ provides a lot of useful information on the this antenna.
The following text is an extract from the attached PDF file.
"End Fed Half Wave Antennas – EFHW ANTENNAS Steve Ellington N4LQ started up a group on Facebook called End Fed Half Wave Antennas. The purpose of this group is to explore the use of an end fed half wave antenna. An end fed half wave antenna is one of a specific length depending on the frequency that it is to be used on, for example, an end fed half wave antenna for 80 meters is about 130′ long. The length of a half wave antenna is calculated using the following formula: L (ft) = 468 / f (freq in mhz). The end fed half wave antenna presents a large impedance to your rig, so this impedance must be stepped down to a more useful impedance that is closer to 50 ohms. Most radios today expect to see an antenna with an impedance of 50 ohms at the end of it. End-fed Half Wave antennas (or EFHWs) cover multiple bands without traps, stubs, or resonators. End-fed wires resonate on their 1/2-wave fundamental frequency plus all odd and even harmonics above. By adding a broad-band matching network, the wire’s high impedance feed point is transformed down to 50 ohms across a wide frequency range and, in most cases, you don’t need a tuner to operate. Note that a single-wire radiator may be installed using only one high center or end support, making it fast and easy to set up at home, on the road, or as a “grab-and-go” emergency antenna. There are many different ways to transform this impedance to 50 ohms. The one that Steve promotes is to use a 49:1 unun and information about this method follows. The following is a diagram which explains how to construct a 49:1 transformer."