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Questions tagged [conditioning]

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3
votes
2answers
74 views

Analytical convergent sequence and numerical divergent sequence

Is it possible to construct a sequence that converges in theory but when computed numerically with a computer program is diverging. I feel that today our computer programs doesn't allow such ...
1
vote
1answer
39 views

Condition number of two perburbation matrix regarding limit and quadtrature integration rules

I have a question regarding the condition number of two different perturbation matrices. To start with let $A$ be a spd matrix with elements defined by $a_{i,j} = \int\limits_{\Omega\subset \mathbb{R}^...
3
votes
1answer
66 views

Condition number of matrix and effects of round off errors

In my numerical linear algebra class, I learned that for some matrices, it could have an element that is a very small number that is approximately 0 (and many orders of magnitude different from all ...
8
votes
1answer
125 views

Central differencing scheme for second derivative leads to ill-conditioning

The central difference scheme: $$\frac{d^2u}{dx^2}=\frac{u_{n+1}-2u_i + u_{n-1}}{\Delta x^2}$$ yields a tridiagonal coefficient matrix [1 -2 1]; As the number of points gets larger, this matrix ...
0
votes
1answer
141 views

What is a relative condition number of a sum of positive values?

We want to compute the relative condition number of: $$x_1+x_2+x_3+\cdots$$ We assume all values are positive, and we will do a limit of a large $x_1=10^{8}$, and smaller values for all the other ...
1
vote
1answer
74 views

Conditioning of matrix factorizations and square roots

For my application, I need factors $\tilde C$ so that $$ \tilde C{}^T \tilde C = C^TMC $$ where $C$ is a long matrix, i.e. $C$ has much more columns than rows, and $M$ is a small symmetric positive ...
13
votes
3answers
3k views

What are the symptoms of ill-conditioning when using direct methods?

Suppose we have a linear system and we know nothing about its conditioning and have no preliminary information about the solution. We blindly apply Gaussian elimination and obtain some solution $x$. ...
6
votes
3answers
138 views

How can I compute the sensitivity index of an expression with a modulus operator in it?

I have a set of equations of the form: $$\begin{align*} x_1&=(ax_0+c) \bmod (m)\\ x_2&=(ax_1+c) \bmod (m)\\ x_3&=(ax_2+c) \bmod (m)\\ &\vdots\\ x_{n}&=(ax_{n-1}+c) \bmod (m) \end{...
15
votes
2answers
960 views

Estimation of condition numbers for very large matrices

Which approaches are used in practice for estimating the condition number of large sparse matrices?
7
votes
3answers
434 views

Does there exist an arbitrary-precision convex optimization solver?

I have a relatively simple convex optimization problem that involves less than 100 variables but contains a terribly ill-conditioned matrix. I have tried CVX and CPLEX; even though both can typically ...