Math Forum / Mathematics / Numerical Analysis / June 2007

A farily standard (pseudocode) computation of machine precision is::
    inverse_radix = 1.0/float_radix
    machine_precision = 1.0
    temp = 1.0 + machine_precision

I work at a company that makes design optimization software. We do a
lot or FEA using commercial tools, and often run the optimization
evaluations in parallel. This makes it easy to run on cheap hardware,
since we get linear speedup and few of the typical parallelization

I get confused of this definition:

can anyone explain about it?
what is it mean? and also where that come from?

Hello. What requirements should be imposed on factors $A_1$, $ B_1$, $ C_1$, $ B_2$, $ C_2$, $ C_3$, that degree polynoms $m \ge 2$ which are own functions of the equation
$$
(A_1 z^2 + B_1 z + C_1) \cdot \frac {d^2 P (z)} {dz^2} +
(B_2 z + C_2) \cdot \frac {d P (z)} {dz} +C_3 P ...

J. G. F. Francis, the one who discovered "QR algorithm" in 1961/1962.
Anybody know if he is still alive? If so, where is he now?
Francis discovered one of the greatest algorithms in the history of
numerical analysis. However, he has apparently never been rewarded for his

I am looking for some direction in the best predictive models for time
series data. The data I am dealing with is the number of rows loaded
to a table once every month. I would like to predict the number of
rows to be processed for an upcoming month, and if the actual rows

Suppose x is a column vector, and v' denotes its transpose, for a quadratic scalar function f
f = x' * A * x
I want to calculate df/dx. Assuming that A is symmetric, we can get
df/dx = 2Ax

I everyone, first of all sorry for my poor english. I need to
concatenate two rotation matrix (in my case the basic rotation matrix
of a beam element and the rotation matrix from the displacements
analisys). The second matrix (rotation from displacements) is coming

 I m trying to solve the Poisson problem
                      \Delta u = f
on the unit square, with Neuman condition on the 4 boudaries:
                       du/dn = g

When I integrate a numerical integral using "quadl" function in Matlab, I
should obtain a smooth curve with varying the parameter tau. But I didn't.
Instead, at some large tau, the integral value becomes jumpy and oscillate
and spiky. What might be the problem? Of course there ...

I am stuck with what first seemed a straightforward Runge-Kutta (4th
order) integration of an ODE of the form dT/dp=C(p,T) T used to
describe an adiabat; T and p are temperature and pressure,
respectively, and C(p,T) are p,T-dependent material parameters. The

I have posted a longer version in MATLAB newsgroup
Anyone know a good correlation technique for FEM displacement v
Measured displacements
that produces an overall single number (0 - 1) ?

Here's my question:  Given a square matrix A, with
k eigenvalues e1, e2, ..., ek, and positive integer r,
are all of the eigenvalues of A^r in the set
(e1)^r, (e2)^r, ..., (ek)^r  ?

I am trying to implement a LaGrange Interpolating polynomial on a set of data. Is there a way to do this without using matrices? The reason is that i need to code this i C++ and i dont want to have to code a matrix dot product into my code. The code itself is already very ...

Hi, there
I have a optimization problem on multiple-time scales with multiple
objective functions
Suppose that we divide [T1, T2] into N time scales: [T1,t2),