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[10] [11] Numarray had faster operations for large arrays, but was slower than Numeric on small ones, [12] so for a time both packages were used in parallel for different use cases. The last version of Numeric (v24.2) was released on 11 November 2005, while the last version of numarray (v1.5.2) was released on 24 August 2006.
Karatsuba algorithm — the first algorithm which is faster than straightforward multiplication; Toom–Cook multiplication — generalization of Karatsuba multiplication; Schönhage–Strassen algorithm — based on Fourier transform, asymptotically very fast; Fürer's algorithm — asymptotically slightly faster than Schönhage–Strassen
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
Geometric Brownian motion is used to model stock prices in the Black–Scholes model and is the most widely used model of stock price behavior. [4] Some of the arguments for using GBM to model stock prices are: The expected returns of GBM are independent of the value of the process (stock price), which agrees with what we would expect in ...
That is an extreme case; in general the formula will understate the total cost of a basket of goods (or of any subset of that basket) unless their prices all change at the same rate. Also, as the index is unweighted, large price changes in selected constituents can transmit to the index to an extent not representing their importance in the ...
Improving part A by a factor of 2 will increase overall program speed by a factor of 1.60, which makes it 37.5% faster than the original computation. However, improving part B by a factor of 5, which presumably requires more effort, will achieve an overall speedup factor of 1.25 only, which makes it 20% faster.
In theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix multiplication can be performed. Matrix multiplication algorithms are a central subroutine in theoretical and numerical algorithms for numerical linear algebra and optimization, so finding the fastest algorithm for matrix multiplication is of major practical ...
The non-asymptotic rate is then an inverse of that number of iterates or computer time. In practical applications, an iterative method that required fewer steps or less computer time than another to reach target accuracy will be said to have converged faster than the other, even if its asymptotic convergence is slower.