Powering White LEDs in Parallel Connections with Boost Converter
Driving the LEDs can be in parallel and/or series connections. It has both their own advantages and disadvantages. A weakness of the parallel connection method
is that LED current and brightness do not automatically match. White
LEDs are popular portable equipment LCD backlights used for such
portable equipment like PDAs, cellphones, and digital cameras. A boost converter (charge-pump, inductor-based), is needed since the battery voltage of most handheld devices is too low for either method.
According to the following article, there are three main methods of driving LEDs parallel connections: using an existing supply for independently regulate the current through each LED, regulate the supply voltage only and rely on LED matching and series resistors for current matching, and matching the remaining LEDs by regulate current through one LED and rely on LED matching and series resistors. For each of those main parallel methods are illustrated in circuit diagrams.
Also, each methods are described in a brief and clear explanations such discussing Integrated LED Current Regulator,
Integrated Charge-Pump Boost Supply and Current Regulator, Mismatches
in LED Current, Dimming Methods, and Converter Regulating Current
Instead of Voltage.
Have a complete read of Powering White LEDs in Parallel Connections with Boost Converter in this LEDs Application Datasheet at page 3-12 from 14 pages of pdf filetype (source: maxim-ic.com).