Iterative Solution of Equations

1994 ◽  
pp. 34-57
Author(s):  
Peter R. Turner
Keyword(s):  
Iterative Solution ◽  
Solution Of Equations

Comparison of lodgepole pine yield tables

1987 ◽  
Vol 17 (9) ◽  
pp. 1110-1114 ◽  
Author(s):  
Alan J. Thomson
Keyword(s):  
British Columbia ◽  
Lodgepole Pine ◽  
Basal Area ◽  
Stand Density ◽  
Iterative Solution ◽  
Variable Density ◽  
Productivity Index ◽  
Stand Development ◽  
Quadratic Mean ◽  
Solution Of Equations

Iterative solution of equations from Johnstone's variable-density yield tables for lodgepole pine permitted estimates of stand development index (DI) and productivity index (PI) from the volume, quadratic mean of diameter at breast height, basal area, or dominant–condominant height associated with a particular stand density at a particular age. Using such estimates, the yield tables of Smithers were compared with those of Johnstone. PI values associated with each of Smithers' site indices were calculated for British Columbia and Alberta. Results suggested that Johnstone's equations could be used in lodgepole pine stands in both British Columbia and Alberta, for PI values from 0.7 to 1.2, for densities up to 2500 stems acre−1 at age 70, and for ages up to 120. This considerably extends the range of application of these equations.

Local block relaxation method for the solution of equations of gasdynamics

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1377-1384
Author(s):  
Carlo de Nicola ◽  
Renato Tognaccini ◽  
Vittorio Puoti
Keyword(s):  
Relaxation Method ◽  
Solution Of Equations ◽  
Block Relaxation ◽  
Local Block

Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

2004 ◽  
Vol 126 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Hakan Ertu¨rk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Design Problem ◽  
Manufacturing Industry ◽  
Three Dimensional ◽  
Chemical Deposition ◽  
Iterative Solution ◽  
Conveyor Belt ◽  
Temperature History ◽  
Transient Temperature

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.

Parallel iterative solution-based tabu search for the obnoxious p-median problem

2021 ◽  
Vol 127 ◽  
pp. 105155
Author(s):  
Jian Chang ◽  
Lifang Wang ◽  
Jin-Kao Hao ◽  
Yang Wang
Keyword(s):  
Tabu Search ◽  
Iterative Solution ◽  
Median Problem ◽  
Parallel Iterative
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