Rapid solution of kriging equations, using a banded Gauss elimination algorithm

1990 ◽  
Vol 8 (4) ◽  
pp. 393-399 ◽  
Author(s):  
J. R. Carr
Keyword(s):  
Elimination Algorithm ◽  
Gauss Elimination

scholarly journals THEORETICAL AND COMPUTATIONAL RESULTS FOR MIXED TYPE VOLTERRA–FREDHOLM FRACTIONAL INTEGRAL EQUATIONS

Fractals ◽  
2021 ◽  
Author(s):  
ROHUL AMIN ◽  
HUSSAM ALRABAIAH ◽  
IBRAHIM MAHARIQ ◽  
ANWAR ZEB
Keyword(s):  
Integral Equations ◽  
Mixed Type ◽  
Fractional Integral ◽  
Haar Wavelet ◽  
Algebraic Equations ◽  
Elimination Algorithm ◽  
Collocation Technique ◽  
Uniqueness Of The Solution ◽  
Gauss Elimination ◽  
Mean Square Errors

In this paper, we develop a numerical method for the solutions of mixed type Volterra–Fredholm fractional integral equations (FIEs). The proposed algorithm is based on Haar wavelet collocation technique (HWCT). Under certain conditions, we prove the existence and uniqueness of the solution. Also, some stability results are given of Hyers–Ulam (H–U) type. With the help of the HWCT, the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Some numerical examples for convergence of the proposed technique are taken from the literature. Maximum absolute and root mean square errors are calculated for different collocation points (CPs). The results show that the HWCT is an effective method for solving FIEs. The convergence rate for different CPS is also calculated, which is nearly equal to 2.

scholarly journals Haar wavelet method for solution of variable order linear fractional integro-differential equations

2022 ◽  
Vol 7 (4) ◽  
pp. 5431-5443
Author(s):  
Rohul Amin ◽  
◽  
Kamal Shah ◽  
Hijaz Ahmad ◽  
Abdul Hamid Ganie ◽  
...  
Keyword(s):  
Differential Equations ◽  
Haar Wavelet ◽  
Variable Order ◽  
Algebraic Equations ◽  
Elimination Algorithm ◽  
Collocation Technique ◽  
Gauss Elimination ◽  
Collocation Scheme ◽  
The Given ◽  
Derivatives Of

<abstract><p>In this paper, we developed a computational Haar collocation scheme for the solution of fractional linear integro-differential equations of variable order. Fractional derivatives of variable order is described in the Caputo sense. The given problem is transformed into a system of algebraic equations using the proposed Haar technique. The results are obtained by solving this system with the Gauss elimination algorithm. Some examples are given to demonstrate the convergence of Haar collocation technique. For different collocation points, maximum absolute and mean square root errors are computed. The results demonstrate that the Haar approach is efficient for solving these equations.</p></abstract>

scholarly journals A Note on Algorithms for Genotype and Allele Elimination in Complex Pedigrees With Incomplete Genotype Data

Genetics ◽  
2000 ◽  
Vol 156 (4) ◽  
pp. 2051-2062
Author(s):  
F-X Du ◽  
I Hoeschele
Keyword(s):  
Markov Chains ◽  
Computational Efficiency ◽  
Genotype Data ◽  
Genetic Analyses ◽  
Cpu Time ◽  
Elimination Algorithm

Abstract Elimination of genotypes or alleles for each individual or meiosis, which are inconsistent with observed genotypes, is a component of various genetic analyses of complex pedigrees. Computational efficiency of the elimination algorithm is critical in some applications such as genotype sampling via descent graph Markov chains. We present an allele elimination algorithm and two genotype elimination algorithms for complex pedigrees with incomplete genotype data. We modify all three algorithms to incorporate inheritance restrictions imposed by a complete or incomplete descent graph such that every inconsistent complete descent graph is detected in any pedigree, and every inconsistent incomplete descent graph is detected in any pedigree without loops with the genotype elimination algorithms. Allele elimination requires less CPU time and memory, but does not always eliminate all inconsistent alleles, even in pedigrees without loops. The first genotype algorithm produces genotype lists for each individual, which are identical to those obtained from the Lange-Goradia algorithm, but exploits the half-sib structure of some populations and reduces CPU time. The second genotype elimination algorithm deletes more inconsistent genotypes in pedigrees with loops and detects more illegal, incomplete descent graphs in such pedigrees.

scholarly journals Converting MST to TSP Path by Branch Elimination

2020 ◽  
Vol 11 (1) ◽  
pp. 177
Author(s):  
Pasi Fränti ◽  
Teemu Nenonen ◽  
Mingchuan Yuan
Keyword(s):  
Spanning Tree ◽  
Closed Loop ◽  
Minimum Spanning Tree ◽  
Travelling Salesman Problem ◽  
Open Loop ◽  
Travelling Salesman ◽  
Elimination Algorithm ◽  
Number Of Iterations ◽  
Number Of Branches

Travelling salesman problem (TSP) has been widely studied for the classical closed loop variant but less attention has been paid to the open loop variant. Open loop solution has property of being also a spanning tree, although not necessarily the minimum spanning tree (MST). In this paper, we present a simple branch elimination algorithm that removes the branches from MST by cutting one link and then reconnecting the resulting subtrees via selected leaf nodes. The number of iterations equals to the number of branches (b) in the MST. Typically, b << n where n is the number of nodes. With O-Mopsi and Dots datasets, the algorithm reaches gap of 1.69% and 0.61 %, respectively. The algorithm is suitable especially for educational purposes by showing the connection between MST and TSP, but it can also serve as a quick approximation for more complex metaheuristics whose efficiency relies on quality of the initial solution.

scholarly journals A sequential elimination algorithm for computing bounds on the clique number of a graph

2008 ◽  
Vol 5 (3) ◽  
pp. 615-628 ◽  
Author(s):  
Bernard Gendron ◽  
Alain Hertz ◽  
Patrick St-Louis
Keyword(s):  
Clique Number ◽  
Elimination Algorithm ◽  
Sequential Elimination
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