Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [convergence]

Questions related to whether the sequence of iterates generated by an iterative method has one or more limit points, and if those limit points have the correct properties.

202 questions
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Convergence rate vs convergence order

I'm a bit confused about the concepts of convergence rate and convergence order. Let me first give you the definitions we use: [sorry for the English, it's all self translated] Let $x^{*}$ be our solution. Definition 1: The sequence $x^{(k)}$ is…
xotix
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The definition of asymptotic convergence?

What is the difference between convergence and asymptotic convergence? Why say the convergence is asymptotic?
JW Xing
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Non-convergance when calculating temperature/heat flows through a section of rock

I am attempting to calculate temperature of section of rock in the earth as a function of vertical position in the rock and time. Along with it I am calculating the heat flow through the rock as a function of vertical position in the rock and time.…
skybluecodeflier
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When and why is `r./sum(r)` not a good way to renormalize a vector in PageRank computation?

I experimented with the PageRank algorithm. When the number of pages is large, I encountered a situation when one formula for re-normalizing a vector (so that sum of its components is equal to 1; elements of the vector are guaranteed to be positive)…
user7610
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Difference between contraction rate and convergence rate

I am slightly confused about the concept of contraction rate. For me it sounds equivalent to a convergence rate. Could somebody clear up the difference for me? I have those two definitions of convergence and contraction rate from the book Numerical…
hcl734
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Computing rate and order of convergence

this is a follow up question to Convergence rate vs convergence order I guess the whole confusion about how rate vs. order of convergence also came from the implementations I saw. For example, for fixpoint iteration, I saw this: [was part ofa…
xotix
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2
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Interpreting convergence study results, fixed CFL

I am trying to determine the order of my numerical method for resolving a fluid-structure interaction problem using the immersed boundary method. I am using Crank-Nicolson to resolve the fluid equations and the immersed body is updated in time using…
namu
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Guess the final term of a converging series

I have a non-linear equation that converges, and reaches suitable accuracy after around 20 steps, however each step is very expensive to calculate. The series are never quite the same, but they are similar; there are 4 examples below. Ideally, I…
user1412633
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What is the Radius of Convergence for analytic functions?

The radius of convergence of any power series can be found by simply using the root test, ratio test etc. I am confused as to how to find the radius of convergence for an analytic $f$ such as $f(z)=\frac{4}{(z-1)(z+3)}$. I can't imagine that I…
Masan
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Convergence of a DASPK depending on DAE formulation

I have a system of non-linear DAE and I noticed that the system does not converge if some of the equations are not differentiated. For example, if the control volume equation is represented as this: $V_{total} = V_1 + V_2$ The solver won't…
Marwan
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Correct order of convergence

I have a sequence of points which was obtained from an iterative algorithm, and I computed the order of convergence $p$ of the method using the formula $$ p \approx \frac{\log({\rm err}(k+2))-\log({\rm err}(k+1))}{\log({\rm err}(k+1)) - \log({\rm…
Julienne Franz
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