mm-276 Subject: Re: Stability of multisteps schemes> Hello!> I found in Prof. John Strikwerda's book Finite Difference Schemes and> Partial Differential Equations theorems about stability of multisteps> schemes (theorem 4.2.1 and 4.2.2.). But unfortunately for me there are> not proofs ot those theorems, but only sketches. I was looking for> this proofs in other books, but only book of Prof. Strikwerda includes> those theorems.> Maybe someone knows where can I find this proofs?> Any help would be very grateful.> John MalySee the books referenced in Notes and Bibliography ofhttp://caswww.colorado.edu/courses.d/FSI.d/FSI.Ch03.d/ FSI.Ch03.pdf(Lecture Notes of a new FSI course in progress). Some books may beavailable at a math/physics/engrg library if you are in a university. If you have a strong math background, I recommend Peter Henrici's ODEbooks for classical (pre-1965) stuff. Else C. W. Gear's book , whichis very readable & covers more ground but skips details. Technicallythe most up to date are the 2 vols of Hairer-Norsett-Wanner, but thatmay be too intensive for what you need. === Subject: fftw compile errors This is driving me crazy.. When I try to compile my program, this happens..I do have #include in my program and I installed FFTW-3.0.1 in the default /usr/local directory.. gcc -o fftw_tst.out fftw_tst.c -lfftw3l -lm/tmp/ccg4aBR0.o(.text+0x187): In function `main':: undefined reference to `fftw_malloc'/tmp/ccg4aBR0.o(.text+0x19c): In function `main':: undefined reference to `fftw_malloc'/tmp/ccg4aBR0.o(.text+0x247): In function `main':: undefined reference to `fftw_plan_dft_1d'/tmp/ccg4aBR0.o(.text+0x260): In function `main':: undefined reference to `fftw_execute'/tmp/ccg4aBR0.o(.text+0x289): In function `main':: undefined reference to `fftw_plan_dft_1d'/tmp/ccg4aBR0.o(.text+0x29a): In function `main':: undefined reference to `fftw_execute'/tmp/ccg4aBR0.o(.text+0x2ed): In function `main':: undefined reference to `fftw_destroy_plan'/tmp/ccg4aBR0.o(.text+0x2fb): In function `main':: undefined reference to `fftw_destroy_plan'/tmp/ccg4aBR0.o(.text+0x309): In function `main':: undefined reference to `fftw_free'/tmp/ccg4aBR0.o(.text+0x317): In function `main':: undefined reference to `fftw_free'/tmp/ccg4aBR0.o(.text+0x325): In function `main':: undefined reference to `fftw_free'collect2: ld returned 1 exit statusany pointers?? Subject: Re: fftw compile errors> This is driving me crazy.. When I try to compile my program, this happens..> I do have #include in my program and I installed FFTW-3.0.1 > in the default /usr/local directory.. gcc -o fftw_tst.out fftw_tst.c -lfftw3l -lm> /tmp/ccg4aBR0.o(.text+0x187): In function `main':> : undefined reference to `fftw_malloc'> [ ... ]These are link errors, so they have nothing to do with having or nothaving the #include in the sources. It seems that you needanother library besides -lfftw3l ? I can't help you beyond that becausewhat I have here is fftw2. I do use fftw3 at work tough. === Subject: Re: fftw compile errors> This is driving me crazy.. When I try to compile my program, this happens..> I do have #include in my program and I installed FFTW-3.0.1 > in the default /usr/local directory.. > gcc -o fftw_tst.out fftw_tst.c -lfftw3l -lm/tmp/ccg4aBR0.o(.text+0x187): In function `main':> : undefined reference to `fftw_malloc'> /tmp/ccg4aBR0.o(.text+0x19c): In function `main':> : undefined reference to `fftw_malloc'> /tmp/ccg4aBR0.o(.text+0x247): In function `main':> : undefined reference to `fftw_plan_dft_1d'> /tmp/ccg4aBR0.o(.text+0x260): In function `main':> : undefined reference to `fftw_execute'> /tmp/ccg4aBR0.o(.text+0x289): In function `main':> : undefined reference to `fftw_plan_dft_1d'> /tmp/ccg4aBR0.o(.text+0x29a): In function `main':> : undefined reference to `fftw_execute'> /tmp/ccg4aBR0.o(.text+0x2ed): In function `main':> : undefined reference to `fftw_destroy_plan'> /tmp/ccg4aBR0.o(.text+0x2fb): In function `main':> : undefined reference to `fftw_destroy_plan'> /tmp/ccg4aBR0.o(.text+0x309): In function `main':> : undefined reference to `fftw_free'> /tmp/ccg4aBR0.o(.text+0x317): In function `main':> : undefined reference to `fftw_free'> /tmp/ccg4aBR0.o(.text+0x325): In function `main':> : undefined reference to `fftw_free'> collect2: ld returned 1 exit status> any pointers??how should the compiler find the library fromgcc -o fftw_tst.out fftw_tst.c -lfftw3l -lmYou better put -L/usr/local/ -lfftw31in this line.Hans Mittelmann === Subject: Re: fftw compile errors> This is driving me crazy.. When I try to compile my program, this happens..> I do have #include in my program and I installed FFTW-3.0.1 > in the default /usr/local directory.. > gcc -o fftw_tst.out fftw_tst.c -lfftw3l -lm/tmp/ccg4aBR0.o(.text+0x187): In function `main':> : undefined reference to `fftw_malloc'> /tmp/ccg4aBR0.o(.text+0x19c): In function `main':> : undefined reference to `fftw_malloc'> /tmp/ccg4aBR0.o(.text+0x247): In function `main':> : undefined reference to `fftw_plan_dft_1d'> /tmp/ccg4aBR0.o(.text+0x260): In function `main':> : undefined reference to `fftw_execute'> /tmp/ccg4aBR0.o(.text+0x289): In function `main':> : undefined reference to `fftw_plan_dft_1d'> /tmp/ccg4aBR0.o(.text+0x29a): In function `main':> : undefined reference to `fftw_execute'> /tmp/ccg4aBR0.o(.text+0x2ed): In function `main':> : undefined reference to `fftw_destroy_plan'> /tmp/ccg4aBR0.o(.text+0x2fb): In function `main':> : undefined reference to `fftw_destroy_plan'> /tmp/ccg4aBR0.o(.text+0x309): In function `main':> : undefined reference to `fftw_free'> /tmp/ccg4aBR0.o(.text+0x317): In function `main':> : undefined reference to `fftw_free'> /tmp/ccg4aBR0.o(.text+0x325): In function `main':> : undefined reference to `fftw_free'> collect2: ld returned 1 exit status> any pointers??how should the compiler find the library fromgcc -o fftw_tst.out fftw_tst.c -lfftw3l -lmYou better put> -L/usr/local/ -lfftw31> in this line.Hans Mittelmannok.. the problem still exitst.. Here is what I have.$$ find /usr/local -name '*fftw*'/usr/local/bin/fftw-wisdom-to-conf/usr/local/bin/ fftwl-wisdom/usr/local/lib/pkgconfig/fftw3l.pc/usr/local/lib/ libfftw3l_threads.la/usr/local/lib/libfftw3l.a/usr/local/lib/ libfftw3l_threads.a/usr/local/lib/libfftw3l.la/usr/local/man/ man1/fftwl-wisdom.1/usr/local/man/man1/fftw-wisdom-to-conf.1/ usr/local/info/fftw3.info-1/usr/local/info/fftw3.info-2/usr/ local/info/fftw3.info-3/usr/local/info/fftw3.info-4/usr/local/ info/fftw3.info-5/usr/local/info/fftw3.info/usr/local/include/ fftw3.f/usr/local/include/fftw3.h $$ cat fftw_tst.c #include #include #include ....snip... the rest of the program ...$$ make gcc -I/usr/local/include -o fftw_tst.out fftw_tst.c -L/usr/local/lib -lfftw3l -lm/tmp/cc2EEH0f.o(.text+0x187): In function `main':: undefined reference to `fftw_malloc'/tmp/cc2EEH0f.o(.text+0x19c): In function `main':: undefined reference to `fftw_malloc'/tmp/cc2EEH0f.o(.text+0x247): In function `main':: undefined reference to `fftw_plan_dft_1d'/tmp/cc2EEH0f.o(.text+0x260): In function `main':: undefined reference to `fftw_execute'/tmp/cc2EEH0f.o(.text+0x289): In function `main':: undefined reference to `fftw_plan_dft_1d'/tmp/cc2EEH0f.o(.text+0x29a): In function `main':: undefined reference to `fftw_execute'/tmp/cc2EEH0f.o(.text+0x2ed): In function `main':: undefined reference to `fftw_destroy_plan'/tmp/cc2EEH0f.o(.text+0x2fb): In function `main':: undefined reference to `fftw_destroy_plan'/tmp/cc2EEH0f.o(.text+0x309): In function `main':: undefined reference to `fftw_free'/tmp/cc2EEH0f.o(.text+0x317): In function `main':: undefined reference to `fftw_free'/tmp/cc2EEH0f.o(.text+0x325): In function `main':: undefined reference to `fftw_free'collect2: ld returned 1 exit statusmake: *** [fftw_tst.out] Error 1still no luck === Subject: settings by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i242Crd13583; by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id i241uhi11658 by legacy.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.10 $, legacy) id i241uhU24821It means there is a conflict in your project settings between how thelibraries you are using were built, and how your project that islinking thme in is built. Try changing your project setting for:Use of MFC:to Use MFC in a Shared DLLand see if this fixes your problem. === Subject: 2D Gamma, 2D Beta Distribution by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i27FEFC17772;Are there 2D Gamma distribution as 2D Gaussian ?Same question for the Beta distribution.Ali === Subject: Total Differential!!Dear all,I understand that the total derivative of a given function z(x,y)=Dz=partialderivative of z with respect to x * dx + partial derive. of z with respectto y* dyBut in one of the math books, the author is referring that the second totaldifferential of a function y(x) as follows d(Dy) d(Dy)D^2y=D(Dy)=fy[ -----*Dx+ ------*Dy] dx dysuch that d(dy)/dx is the partial derivative of Dy to x and so on.Which means that y is both a function of x and a function of itself??Which implies that the differential of y(x) is not dyDy= ---*Dx dxbut becomes as follows dy dyDy= ---*Dx+---*Dy, is this possible??. dx dxI know that according to chain rule in case of implicit functions if weassume that y(x) is a function of itself say u(y), which is a function of x dy du(y) d(y(x))Then ----= -----*------ dx dy dxand hence if we have an implicit function like y^2=xtaking the derivatives wrt x for both sides of the equation will yield to 2ydy/dx=1therefore dy/dx=1/(2y),Can we apply the same concept to get the total derivative by assuming that yis a function of itself u(y) , which is in turn a function of x.(i.e. Total differential of y= partial derivative of y with respect toitself * dy+ partial derivative of y with respect to x* dx)And what does it mean in this case??Thank you very much.P.S : this argument is found in Chiang book Fundamental Methods ofMathematical Economics Page 380. === Subject: Determining coefficients for basis function by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i27MXBP27495; I am trying to determine coefficients p,q,and r for the functionspace, functions of which are linear combination of 1, x and x^2 andthey satisfy the following equation: f<1st derivative>(2) = p*f<1st derivative>(1) + q*f<2ndderivative>(1) + r*[(x*f(x))dx] ....[Eq 1]I don't see how I can generate 3 equations to determine 3coefficients. The only equation I can set up is taking a functionwhich is a linear combination of the elementary elements above, say,f(x) = p*1 + q*x + r*x^2, find the first derivative at x=1,x=2 andsecond derivative at x=1 and the intergration and plug them in [Eq 1].But how where would I get the other 2 equations from? === Subject: Re: Determining coefficients for basis function > I am trying to determine coefficients p,q,and r for the function >space, functions of which are linear combination of 1, x and x^2 and >they satisfy the following equation: > f<1st derivative>(2) = p*f<1st derivative>(1) + q*f<2nd >derivative>(1) + r*[(x*f(x))dx] ....[Eq 1] >I don't see how I can generate 3 equations to determine 3 >coefficients. The only equation I can set up is taking a function >which is a linear combination of the elementary elements above, say, >f(x) = p*1 + q*x + r*x^2, find the first derivative at x=1,x=2 and >second derivative at x=1 and the intergration and plug them in [Eq 1]. >But how where would I get the other 2 equations from? >you obviously misunderstood the problem. try to find p,q,r such that the equation holds for f(x)=1, f(x)=x and f(x)=x^2 then it holds for any polynomial of degree two at most (why?) does it hold for third degree polynomials?hthpeter === Subject: test (plz ignore) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i27MXFB27618;I sent a message couple of hours ago but didn't go through. Wonderwhy? So just testing to see if it's working now. === Subject: A problem in ANSYS by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i27MXDs27548;I want to solve the problem of dynamic impact analysis on a metalcylinder block. I want to involve dynamic contact (like in automobilecrash study). Can anybody help me as to how to aproach the problem? === Subject: Re: iterative methods for solving systems of linear equations to all of you guys... your links helped me a lot...so thank you: spellucci, zeeuw, wolinsky...and similargood-links-providers... thank you...see you around... and ones more, you deserve it ; )P.S. Herr Stahel, you can mail me answer to krunom@hotmail.com. === Subject: Re: Boundary Value Problem> I'm not sure I can explain this very well.> I need to write a program that solves a BVP by finite differences.> I have done this sort:-u''(x) + c(x)u(x) = f(x) ( u(0) = gamma0, u(N) = gamma1)> with an appropriate gamma0 and gamma1.When solving this, I end up with a matrix A (I hope someone knows what> I'm talking about) which looks like this for one line:> (-1 2+c(x)*h^2 -1 )u = fI would like to know what the Matrix A looks like when solving a> general boundary value problem:-(a(x)u'(x))' + c(x)u(x) = f(x)Please someone help me!> There are several levels of sophistication one can employ indiscretizing this sort of differential operator, depending uponwhat you want to assume about the variation of your functionsa, c and u between the meshpoints. See my discussion in:http://www.utdallas.edu/~frensley/technical/qtrans/node7. htmlThis concerns the Schroedinger equation in a medium with varyingeffective mass, but the equations are equivalent. === Subject: Re: How To Solve An Exponential Equation (Bleasdale Model) >I have 3 data points, where x=1,2,3, and y3>y2>y1 >I am trying to fit these to the Bleasdale Model, where: >y=(a+bx)^(-1/c) >I arrive at the folllowing equation, where p, q, and r are known, and >I need to solve for B: >(1+B)^p*(1+2B)^q*(1+3B)^r=1 >How can I solve for B? If it helps, B is always between 0 and 1 for >my application. >Jimassuming that a solution exists (exponents of different sign present)this is an equation in one unknown. it should be possible to find a crude intertval which encloses a zero (make a crude table and search for a sign change), then use zeroin from http://www.netlib.org/fmm(this is fzero in matlab)hthpeter === Subject: Re: How To Solve An Exponential Equation (Bleasdale Model)p, q, and r are not all positive or negative, and B=0 is not a meaningful result. Any ideas on how to proceed?JimI have 3 data points, where x=1,2,3, and y3>y2>y1I am trying to fit these to the Bleasdale Model, where:y=(a+bx)^(-1/c)I arrive at the folllowing equation, where p, q, and r are known, and> I need to solve for B:(1+B)^p*(1+2B)^q*(1+3B)^r=1How can I solve for B? If it helps, B is always between 0 and 1 for> my application.JimAre p, q and r all positive or all negative? If so, B = 0 .Only if one of the exponents has the opposite sign from the> others is there a non-trivial root. Does this help?> -- > Julian V. Noble> Professor Emeritus of Physics> jvn@lessspamformother.virginia.edu> ^^^^^^^^^^^^^^^^^^> http://galileo.phys.virginia.edu/~jvn/ God is not willing to do everything and thereby take away> our free will and that share of glory that rightfully belongs> to us. -- N. Machiavelli, The Prince. === Subject: Re: equation II buuu !!!!!! >y' = _3 * y^(3/2) +1 >y(0) = 1 >can someone plz tell me what is the resalt for this eqation? or at least >what method should i use ? >thx in advance:) >Kasia >dy/(3*y^(3/2)+1) = dxint_{y0 to y} d w/(3*(w^(3/2)+1) = int_{x0 to x} dx = x-x0w=(1/(3^(2/3))) u^2u/(u^3+1) = Cu/(u+1)+(Au+B)/(u^2-u+1) = ...........calculus first term ...hthpeter === Subject: Re: Nonlinear curve fitting help needed> I need to fit a loose 'best fit' curve so that given an x of 200 (for> example) I can give a realistic estimate of what y should be.Run your data through the 2D function finder at http://zunzun.com James Phillips http://zunzun.com === Subject: Re: Nonlinear curve fitting help needed >First, I am not a mathematician (clearly)- its been too long since I took >calculus! >Second this is -not- homework >I need to fit a curve to a data set so that I can interpolate potential >points. >For example, if I have: >x = {100, 130, 135, 150, 164, 180, 300, 310 } >y = {20, 25, 27, 35, 34, 45, 30, 28 } >I need to fit a loose 'best fit' curve so that given an x of 200 (for >example) I can give a realistic estimate of what y should be. >I also need to be able to adjust how 'tightly' the curve fits the data >points. For example, if the curve fits too tightly on the data, then >somewhere between 180 and 300 on the x axis the y will either approach or >become 0, which is wrong for my purposes. >I need to implement this in C++, so I need the formulas and calculations to >use, if all I have to start with are my x[] and y[]. >Can anyone either help out directly or point me to a good site that will >help me out? >Bryan >first of all: you are sure that the pair (180,45) is not an outlier?if you can assume that all your points have equal precision and oyu have no idea which kind of fit to use, then a least squares spline would be most appropriate,this can finally be made interpolating, if you want, by simply adjusting the bounds on the fiterror. you find least squares splines athttp;//www.netlib.org/tomsandhttp://www.netlib.org/ dierckxhthpeter === Subject: Re: Hexagonal and pentagonal finite element: > : > : > Sorry I have never considered 6 or 5-sided 2D or (prismatic) 3D: > : > elements. I think you will have difficulty finding a mesh-generatator: > : > which produces tesselations using these elements. But that is more of: > : > a practical issue.: > : > : Somebody is claiming to have something working, I'll ask him if he can : > : provide source code.: > : Mathieu: > : > It is really a trivial problem, you dualise a tetraedon mesh. You obtain : > then a mesh where each node belongs exactly to 4 elements.: The problem with this approach is when you are using a 5-node pyramid: as a transition element between an 8-node hex and other tetrahedra. : Splitting the pyramid as you recommend generates a hanging edge and: thus a non-conforming mesh, the thing you were trying to avoid in the: first place.: -JohnDon't really understand what you mean. We have such a mesh generator inCast3M (and the corresponding elements with a generalized formulation).The only problem is on the surface of the domain. You need to take precautions to insure convexity of elements.Pierre Verpeaux === Subject: FFT and zero paddingI am trying to understand the usage of FFT for polynomial multiplication. I am not able to understand the way zero padding is done.Pls let me know which of these 2 ways its done.1. Suppose we have coefficient vectors of two polynomials (of equal degrees)that we have to multiplyA = [a1, a2, ... , an] andB = [b1, b2, ... , bn] and W = [W1, W2, W3, ... , Wn, ..., W2n]are 2n complex (2n)th roots of unity.Now if n is not a power of 2 then we pad with, leading zeros, all the 3 vectors to the nearest power of 2. GettingA' = [0, 0, 0, 0, ... , a1, a2, ... , an] B' = [0, 0, 0, 0, ... , b1, b2, ... , bn]andW' = [0, 0, ... , W1, W2, W3, ... , Wn, ..., W2n]Now perform fft routines on A' B' using W' 2.Zero Pad with leading zeroes A and B A' = [0, 0, 0, 0, ... , a1, a2, ... , an] B' = [0, 0, 0, 0, ... , b1, b2, ... , bn]suppose the new length of the vectors is n' = 2^k for some know compute 2n' complex roots of unity W2n' = [W1, W2, W3, ... , W2n'] Now perform FFT on A' and B' using W2n' === Subject: Optimisation where constraint A OR constraint B must be trueI have a convex optimisation problem with a quadratic objective, a fewlinear constraints and a lot of quadratic constraints. I can solve thisusing SQP (specifically NAG routine E04UCF, which I think is the same asNPSOL).I want to extend this such that each of the quadratic contraints is replacedby two quadratic constraints. However, I do not need both constraints to besatisfied, it is suffiecient if either one or the other (or both) is/aresatisfied. Can anyone point me to suitable software or literature?The only idea I currently have is to replace(A>0) OR (B>0)with something likeA + a*exp(B/b) > 0which, for suitable a and b, might be sufficiently close to the constraintsI want to impose. However, I was hoping for a more elegant solution.-- Dr Andrew McLeanMarine and Acoustics CentreQinetiQ ltdThe views expressed above are entirely those of the writer and donot represent the views, policy or understanding of any otherperson or official body. === Subject: Re: Optimisation where constraint A OR constraint B must be true> I have a convex optimisation problem with a quadratic objective, a few> linear constraints and a lot of quadratic constraints. I can solve this> using SQP (specifically NAG routine E04UCF, which I think is the same as> NPSOL).I want to extend this such that each of the quadratic contraints is replaced> by two quadratic constraints. However, I do not need both constraints to be> satisfied, it is suffiecient if either one or the other (or both) is/are> satisfied. This is called a disjunctive constraint; maybe this helps you searchfor it. Disjunctive constraints destroy the convexity of yourproblem; the standard way to model them is to introduce additionalbinary variables.> Can anyone point me to suitable software or literature?Maybe my survey Complete Search in Continuous Global Optimization and Constraint Satisfaction, http://www.mat.univie.ac.at/~neum/papers.html# glopt03helps.Arnold Neumaier === Subject: Re: Try thisI have a question: how is AOL these days? Still full of losers? === Subject: Examples using IMSL for non-linear curve fittingThe IMSL for FORTRAN library has routines to perform non-linear least squarecurve fitting. Is there any example FORTRAN code using IMSL for non-linearcurve fitting available so I can learn how to use the library. I will useCVF 6.6. a === Subject: Re: Examples using IMSL for non-linear curve fitting> The IMSL for FORTRAN library has routines to perform non-linear least square> curve fitting. Is there any example FORTRAN code using IMSL for non-linear> curve fitting available so I can learn how to use the library. I will use> CVF 6.6.> a lotThe user guides at include examples of use.-- Dave SeamanJudge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Round off example: MATLAB ok, GCC not okGreetings!The algorithm below is unstable underMATLAB since the number 2.1 has an infinite binary expansion. I've tried to reproduce the same behaviour under GCC but, no luck, it's stable withthe famous C compiler. What's happening? Is it possibleto make GCC to act like MATLAB? Am I missingsome compiler directive? in advance, Humberto.---------------------------------------format longx = 2.1;y = 2.1;for i = 1:40 z = 4.0*x - 3.0*y x = y; y = z;end--------------------------------------- === Subject: Re: Round off example: MATLAB ok, GCC not ok> Greetings!> The algorithm below is unstable under> MATLAB since the number 2.1> has an infinite binary expansion.> I've tried to reproduce the same behaviour> under GCC but, no luck, it's stable with> the famous C compiler.> What's happening? Is it possible> to make GCC to act like MATLAB? Am I missing> some compiler directive?> in advance, Humberto.> ---------------------------------------> format long> x = 2.1;> y = 2.1;> for i = 1:40> z = 4.0*x - 3.0*y> x = y;> y = z;> end> ---------------------------------------The Gnu compiler is pretty agressive about optimizing -- I could believethat it would see that x and y are equal, and therefore that z = y already,and basically optimize your whole loop to nothing.You can try to turn optimizations off, but I've had that compiler optimizesome anyway (maybe it's streamlining, not optimization).If you want to absolutely _force_ it to make the computation put the 4.0 *x - 3.0 * y into a function call, or declare x and y to be volatile (thefunction call would be a stronger way to do it).----------------------------------------Tim WescottWescott Design Serviceshttp://www.wescottdesign.com