Final answer:
Without the specific context of Pan's matrix multiplication algorithm, it's not possible to determine the correct recurrence relation for its worst-case complexity from the given options. Recurrence relations describe how each term in a sequence is derived from the previous ones and are essential for understanding the efficiency of recursive algorithms.
Step-by-step explanation:
The question asks to identify the recurrence relation for the worst-case complexity w(n) of Pan's matrix multiplication algorithm. A recurrence relation describes how to construct the sequence of complexity terms from previous terms. For example, the relation w(n) = 2w(n-1) would imply multiplying the previous term by 2 to get the current term, and so on. This kind of relation is often used in computer science to characterize the efficiency of algorithms, especially recursive algorithms.
However, without specific context on Pan's matrix multiplication algorithm, it is not possible to ascertain which of the given options a), b), c), or d) is correct. The recurrences deal with different operations: multiplying by a constant, adding a linear term, or using a quadratic term, all of which signify different algorithmic strategies and efficiencies. Based on general knowledge, popular matrix multiplication algorithms, like Strassen's algorithm, employ a 'divide and conquer' strategy, which tends to have a recurrence relation involving both a multiplication term and an additive term (i.e., adding a function of n) as seen in option c). Nonetheless, without the specific details for Pan's algorithm, this cannot be confirmed.