What is the complexity of matrix multiplication algorithm for multiplying a square matrix to square matrix?

What is the complexity of matrix multiplication algorithm for multiplying a square matrix to square matrix?

As of December 2020, the matrix multiplication algorithm with best asymptotic complexity runs in O(n2.3728596) time, given by Josh Alman and Virginia Vassilevska Williams, however this algorithm is a galactic algorithm because of the large constants and cannot be realized practically.

What do you mean by time and space complexity of an algorithm?

Time complexity is a function describing the amount of time an algorithm takes in terms of the amount of input to the algorithm. Space complexity is a function describing the amount of memory (space) an algorithm takes in terms of the amount of input to the algorithm.

What is the runtime complexity of matrix multiplication?

This is a major open question in theoretical computer science. As of December 2020, the matrix multiplication algorithm with best asymptotic complexity runs in O(n2.3728596) time, given by Josh Alman and Virginia Vassilevska Williams.

What is the time complexity of the matrix multiplication and Strassen’s algorithm?

Hence, the complexity of Strassen’s matrix multiplication algorithm is O(nlog7).

How can I improve the time complexity of multiplication?

Time complexity of multiplication can be further improved using another Divide and Conquer algorithm, fast Fourier transform. We will soon be discussing fast Fourier transform as a separate post. The above program returns a long int value and will not work for big strings. Extend the above program to return a string instead of a long int value.

How to multiply two integers in less time complexity using divide and conquer?

Using Divide and Conquer, we can multiply two integers in less time complexity. We divide the given numbers in two halves. Let the given numbers be X and Y.

What is the total time complexity of the algorithm in example 1?

From the facts above follows that the total time complexity of the algorithm in Example 1 is $O (N^2.MN) = O (MN^3)$. Let’s take an another example.what will be running time complexity of following code?

Is multiplication constant-time or variable-time operation?

Multiplication of fixed-size numbers (such as int in most C++ implementations) is by definition constant-time operation. The input is always of the same size (same number of bits) so computation time as a function of input has a hard upper bound. Multiplication of arbitrary-precision numbers is another matter.