Multiple algorithm

Multiplicative algorithms (ISRA, RLA and EM) are very popular (mostly RLA in astronomy) because they are very simple to implement and their very first iterations are very efficient. Otherwise their convergence is much slower... 

Lanteri, H., Roche, M., and Aime, C., 2002, Penalized maximum likelihood image restoration with positivity constraints multiplicative algorithms. Inverse Problems 18, 1397... 

Other docking algorithms such as Glide [33], Dock [34] and GOLD [35] have also been used to predict the site of metabolism, and a recent study compared the performance of multiple algorithms in the field of cytochrome P450s [36],... 

Figure 8. Pictorial representation of the outer product matrix multiplication algorithm. ...

Bishop, T. C., Skeel, R. D. and Shulten, K. (1997). Difficulties with multiple time stepping and fast multiple algorithms in molecular dynamics. J. Comp. Chem., 18, 1785-1791. 

Exponentiation can be computed efficiently in any family of groups where an efficient multiplication algorithm is given, due to the well-known square-and-multiply algorithm. It needs / squarings and, on average, / /2 multiplications for an / -bit exponent. 

Main public key test mkjest (on input ( 1 , V, prek, mk) with prek = (q, p, g, g ) and mk = (mki, mk2)) Instead of testing that mki elements of Hgp, it is usually sufficient to test that they are in Zp The length restrictions are still fulfilled, and the only other property that could be violated by enlarging the set of acceptable main public keys is that test works in polynomial time for all public keys.that can possibly occur, and any usual multiplication algorithm works on the entire Zp. 

We will illustrate parallel matrix-vector multiplication algorithms using collective communication in section 6.4, and detailed examples and performance analyses of quantum chemistry algorithms employing collective communication operations can be found in sections 8.3,9.3, and 10.3. 

From Eq. 6.10 it follows that the dimension n must grow at the same rate as p to maintain a constant efficiency as the number of processes increases. If n increases at the same rate as p, however, the memory requirement per process n /p + 2n) will increase with the number of processes. Thus, a fc-fold increase in p, with a concomitant increase in n to keep the efficiency constant, will lead to a fc-fold increase in the memory required per process, creating a potential memory bottleneck. Measured performance data for a parallel matrix-vector multiplication algorithm using a row-distributed matrix are presented in section 5.3.2. 

Let us try to modify the matrix-vector multiplication algorithm from section 6.4.1 to improve the scalability. The poor scalability was a result of the relatively large communication overhead incurred by using a row distribution for the matrix A. When A is distributed by rows, all elements of the b or c vector must visit (or be stored by) each process during the computation if b and c are replicated, no data exchange is required for b, but an all-to-all broadcast is required to replicate c at the end of the computation if both vectors are distributed, no communication is required for c but all elements of b must visit all processes during the execution. 

In order to evaluate HETA, two case-study applications based on a 6 x 6 matrix multiplication algorithm and a bubble sort classification algorithm were chosen to be hardened. 

There is a consensus that type I and III leaks should be treated on a relatively urgent basis. There is still debate regarding the treatment of stable type II leaks. Multiple algorithms are proposed for the treatment of the endoleaks (Table 14.2). In this chapter, we will discuss the treatment options for each type of endoleak separately. 

For the presented examples and based on the multiplication algorithm proposed in (Bryant et al 1995) we have not been able to get beyond word sizes of 64 bit. The time requirements for bit selection grow exponentially with the word size. Using the Apply algorithms presented in this paper, word sizes of up to 256 bit could easily be handled. 

Wheeler, R., Aitken, S. (2000). Multiple algorithms for fraud detection. Knowledge-Based Systems, 73(2-3), 93-99. 

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