As Demmel and others have noted, SVD is both more reliable and more expensive than QR as a method of solving rank-deficient least squares problems.

SVD is the method that LinearAlgebra:-LeastSquares will choose when the Matrix has more columns than rows (n>m), unless instructed otherwise using the optional 'method' parameter.

LinearAlgebra:-SingularValues always computes a full U and Vt. But for least squares computations, such as when n>m, this is not necessary. Including the smaller singular values may just be (re-)introducing noise. See here for more detail.

Here's a 20x2000 example, using wrapperless external calling and the SVD routine dgesvd in the CLAPACK library. The effective speedup by using the Thin SVD for that 20x2000 least squares example is about a factor of 100 (ie, 2000/20), with a similar reduction in additional memory allocation.

I have found this problem somewhere in a math forum: somebody wanted to simplify this expression ( I write it in maple syntax:, this was not a maple forum):

a:=(1253*sqrt(2)-963*sqrt(3))^(1/3)+(26209+10500*sqrt(6))^(1/4);

They tried with the simplify command of maple, but it didn't work, and they tried with Fullsimplify command of the other famous math program , and it worked. ( I haven't tried it.) The conclusion was that Maple couldn't do this job.

Actually Maple can do this job with radnormal:

radnormal(a);

14*2^(1/2)

I am having problems using implicitplot.  I run this code and it worked and today I tried it again and it gives me the following:

with(plots,implicitplot);

implicitplot(0=int(erf(  (T-e*t)/sqrt(2)  )*t^2*exp(-t/2),t=0..infinity),e=0..1,T=0..10);

Error, (in plots/implicitplot) invalid input: the following extra unknowns were found in the input expression: {t}

The weird thing is that this worked before (took about 10min though) and now it isn't.  Any suggestions?

Thanks

 

I am trying to plot q2:= (x) -> x*exp(x^2)*(1-erf(x)); for 0 <><>plot(q2(x),x=.1..10); then the resulting plot is incorrect. In reading other posts I get the impression that one needs to somehow prevent the plot routine(s?) from following their default behavior of refusing to compute with the

What is the big oh of the binomial coefficient

  n

(   )

  k

Hi, I'm hoping someone in here will be able to help me.

I've made two files in which I need to find a symbolic expression for the difference between two mathematical models of a mass, damper, spring system:

Hi,

            I have a question regarding  Chebyshev interpolation of data. How can I interpolate the following data by Chebyshev interpolation using maple?

X:=[16,45,85,120];
Y:=[4,7.2,1.6,0.5];

Thank you

 

I want to have a procedure define a function... If I do: >with(stats); >does_not_work:= proc(t) local v,d0,d1,x,y; > v = rhs(fit[leastsquare[[x,y], y=d0+d1*x]](t)); >end proc; then > does_not_work([[0,1,2],[3,4,5]]); results in "v = 3 + x" as expected, but if I try to have the procedure define a function d as in >does_not_work:= proc(t) local v,d0,d1,x,y; global d; > v = rhs(fit[leastsquare[[x,y], y=d0+d1*x]](t)); > d:= (x) -> v; >end proc; then > does_not_work([[0,1,2],[3,4,5]]); > d(1); does not result in 4, which should be the result of applying

Okay, I'm just really starting to get into Maple again, but I'm having a little trouble getting a package to work.

I'm trying to take a look and review the precalculus package from the application center but it doesn't seem to work. 

It's from maple 7.  The new version doesn't seem to follow through on the commands made.

Hi there :) As i am new here first a short Hello: Hello, my Name is Gernot, and i am Physics Student of the 6th Semester. I am a beginner in Maple, and am prety new to Calculating on the Computer in General. At the moment i need Maple primary for calculations and analyzing Measuring Data from the Exoeriments in my Physics practica. And I have some Questions on that, and hope you can Help me a bit :) As i don't want to do a Monster Posting here, i will make more Topics on ym Questions, although they all stick together ;). So my first question is: I am Having a Vector

Please help me solve these two problems please past the code for maple 11.

2. For the function

f

hi, what code do I use to sum the number of heads from a random coin toss to illustrate the Central limit theorem (relationship between the binomial and normal distribution). The more approachable the code is the better..

I'm very confuse with this question:

- Find one root/zero of  2*x^5-5*x^4+3*x^3-3*x^2+x+2 using Newton's Method. If your polynomial is sadly lackaing in a root, subtract some constant value until the polynomial cuts the x-axis

- Produce four iterations of the Newton's Method. This will result in four successively accurateapproximations to one solution of p(x)=0

- For each iteration, report your beginning x_n and the subsequent x_n+1 value. For each run, also product a graph of p(x) and the graph of the newest Newton created tangent line

solve({x11*x11+x12*y11+x13*z11=x11*x11+x12*x21+x13*x31,

x11*x12+x12*y12+x13*z12=x11*x12+x12*x22+x13*x32,

x11*x13+x12*y13+x13*z13=x11*x13+x12*x23+x13*x33,

 

x11*x21+x12*y21+x13*z21=x21*x11+x22*x21+x23*x31,

x11*x22+x12*y22+x13*z22=x21*x12+x22*x22+x23*x32,

x11*x23+x12*y23+x13*z23=x21*x13+x22*x23+x23*x33,

 

x11*x31+x12*y31+x13*z31=x31*x11+x32*x21+x33*x31,

Warning, computation interrupted

 

> solve({x11*x11+x12*y11+x13*z11=x11*x11+x12*x21+x13*x31,

x11*x12+x12*y12+x13*z12=x11*x12+x12*x22+x13*x32,

x11*x13+x12*y13+x13*z13=x11*x13+x12*x23+x13*x33,

 

x11*x21+x12*y21+x13*z21=x21*x11+x22*x21+x23*x31,

x11*x22+x12*y22+x13*z22=x21*x12+x22*x22+x23*x32,

x11*x23+x12*y23+x13*z23=x21*x13+x22*x23+x23*x33,