Germany's central bank has said that the country's economy is on track to avoid a recession as it shows signs of growth in the first three months of the year.

Europe's largest economy shrank 0.6% in the last quarter of 2012. Two quarters of falling output in a row is a common definition of recession.

The Bundesbank said in its monthly report, published today, that increasing business optimism and easing fears about the government debt crisis among the 17 euro zone countries mean business may become more willing to invest and expand.

That means that "a plus in total economic production can be expected for the first quarter of 2013'', it said.

A growing German economy could help speed the euro zone's recovery, which is mired in recession. Governments are cutting spending and raising taxes to reduce heavy levels of debt, slowing their economies.

Greece, Portugal and Ireland have needed bailout loans from the other euro zone members, while Spain and Italy are in recessions with high unemployment levels.

The European Central Bank has said that the euro zone will shrink 0.3% in 2013 and only start to recover later in the year.

Growth is key for solving the debt crisis, since it shrinks the size of country's debts relative to their economy and increases revenue from income and business taxes.

German growth helps the other countries in the euro zone because German consumers purchase imports from them, and because German companies use firms in neighbouring countries as suppliers.