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Basically, it takes around 14V to charge a 12V battery, so its yes but to be at safe side, you will need a charge controller whereby it controls the charging current into the battery to prevent the battery from overcharged.
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Charging directly with 16V can be dangerous as there is no charging control.
Typical battery charger uses a 12V, 25W lamp as a series resistor. This way battery voltage cannot reach more than ~13.5 V while charging. No more regulation is needed and you can use your 16 V power supply. Make sure the supply can deliver at least 5-6 A into a discharged battery.
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