Elimination algorithms

Thus, we have proved that under conditions (16) the right elimination algorithm is correct, meaning nonzero denominators in formulae (11), (12) and (15). So, under conditions (16) problem (9) has a unique solution given by formulae (10)-(15). 

A serial elimination algorithm was first proposed by Ripps (1965) and extended later by Nogita (1972). This approach eliminates one measuring element at a time from the set of measurements and each time checks the value of a test function, subsequently choosing the consistent set of data with the minimum variance. In this case, after a new measurement has been deleted, the test function and the variance for the resulting system have to be recomputed when the number of suspect measurements is increased, this may become a laborious solution. 

Alternatively, the number of desired compounds can be predefined and a stochastic algorithm used to maximize the diversity of the selected set, although these methods are even slower than addition methods. Sphere-exclusion methods, which Pearlman calls "elimination" algorithms because the diverse subset is created by eliminating compounds from the superset, have been implemented in Diverse-Solutions (31) (see Section 2.2.1.1), providing a rapid distance-based diverse subset selection method. The minimum distance between nearest neighbors within the diverse subset is first defined a compound is chosen at... 

For this aim, Lindborg et al [119] used a coupled solver in combination with the partial elimination algorithm (PEA) proposed by Spalding [177]. The combined PEA-coupled solver used in their work is outlined in the following. 

To deal with the strong coupling between the phasic momentum equations, the partial elimination algorithm (PEA)-method proposed by Spalding [18, 19] is frequently used. 

For this simple example with only three unknowns, we could calculate the product A b by hand however, for systems with a large number of unknowns, this is not practical. For a dense matrix A, one with mostly non-zero values, the normal way to calculate A b is the general Gaussian elimination algorithm [4]. This algorithm takes a number of mathematical operations that is proportional to n where n is the number of unknowns. 

Gaussian elimination Algorithm that solves a linear system of equations via successive elimination of its unknowns, or, equivalently, via decomposition of the input coefficient matrix into a product of two triangular matrices. 

The forward-elimination algorithm can be immediately extended to overdetermined and underdetermined systems. 

Elimination Algorithms Make Large-Scale Protein Side-Chain Stmctnre Prediction Tractable Implications for Protein Design and Structural Genomics. 

For image analysis semi-automatic bone-segmen-tation/elimination algorithms can be used (Figs. 10.4c and 10.5a). There are different approaches to bone-elimination The most commonly used algorithms... 

In order to reduce the false positive detection, the interslice noise elimination algorithm is employed. The aim of inter-slices analysis is to improve the accuracy of lesion regions detection. In general MRI screening, the position of a lesion may not change drastically between MRI slices. Based on this study, the centre of mass of detected lesion region between current and next slices is compared [11]. Equations (2), (3) and (4) evaluate the centre of mass for lesion regions and eliminate non SD-connected objects. 

Karki KC, Patankar SV (2004) Application of the partial elimination algorithm for solving the coupled energy equations in porous media. Numer Heat Transf Part A 45 539-549... 

The above formulas complete the solution of the equations by the Gauss elimination method by calculating all the unknowns from to x,. The Gauss elimination algorithm requires n /3 multiplications to evaluate the vector jc. 

The MATLAB elimination solver , also known as the midivide function, can handle matrices stored in sparse-matrix format. If the matrix is banded, the bandwidth is determined and the elimination algorithm modified accordingly. If the matrix is not banded, the solver attempts to reduce the bandwidth as much as possible by applying a hemistic algorithm that interchanges rows and columns. 

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