Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later

Key Points

• The aim is to explore different methods to compute the exponential of a matrix and evaluate their practical effectiveness.
• Review of historical and modern methods for calculating matrix exponential.
• Consideration of computational stability and efficiency in method selection.
• Analysis of developments in the field since 1978.
• No method completely satisfies both computational stability and efficiency.
• Certain methods show better practical performance than others, despite limitations.
• The paper incorporates updates and recent advancements in matrix exponential computation.

Abstract