mm-111
Will I be able to run Mathematica on my Pentium 133
Mhz computer?Does it need X11 or may I run it from the
console?Michele
=I downloaded about 1 year ago MockMMA but
couldnt compile it with the GNU Lisp. Can you address me to
a Lisp compiler suitable for the task and perhaps open
source?Michele
=It has been run on older versions of GCL,
but was written forAllegro Common Lisp, which you can get
free/trial version if youdont have it otherwise. There are
only 3 places where MockMMA differs from the ANSI standard.1.
It uses a program (errorset, I think) not in ANSI Lisp, whose
useshould be conditionalized out.2. It prefers to use a lisp
in which upper and lower case are different,as they are in
Mathematica. That is Sin and sin are different. I thinkthis
issue is also avoidable.3. I think there is some part of
unique hash-coding cons that was done especially efciently
in Allegro, but could be done in an ANSI versionin le
consalt.You could explain what problem you have compiling
(probably just to theauthor :)Regarding your other question,
I think you should ask the Mathematicapeople.> I downloaded
about 1 year ago MockMMA but couldnt compile it with the GNU
> Lisp. Can you address me to a Lisp compiler suitable for
the task and > perhaps open source?> > Michele
=written in
Pascal.Currently (version 0.40a) its only a numerical tool,
but I now would like to improve it and make it a true cas.I
saw the book Modern Computer Algebra, but dont know wheter
it shows good algorithms for my purpose. I already have
Knuths Seminumerical Algorithms and will probably go on
with it, without buying others books, anyway Ill be happy if
some of you will give me an hint.Michele
[...] > I saw
the book Modern Computer Algebra, but dont know wheter it
shows > good algorithms for my purpose. I already have
Knuths Seminumerical > Algorithms and will probably go on
with it, without buying others books, > anyway Ill be happy
if some of you will give me an hint.I also saw Modern
Computer Algebra in a bookstore and was impressed.Heres its
web site with some content samples available for
download:http://www-math.uni-paderborn.de/mca/Computer
Algebra Handbook by Grabmeier/Kaltofen/Weispfenning might
beworth a consideration. Less implementation-oriented, but
gives a surveyof the state-of-the-art.-- Thomas RichardMaple
SupportScientic Computers GmbHhttp://www.scientic.de
All inequalities?> > Your particular example can be solved
by> trying to> > solve(2^n-n^2=0), which has 3 roots n=4, n=2
and> n = - ((2 * lambert_w(((log(2))/2)))/(log(2)))> which is
about n=-0.76666.> Thus one can deduce that the expression
does not change sign after> n=4. try n=5, when 32>25 so it is
positive.> > Thus the statement below can be proved, if you
can state it> as given above.> > I do not know if there is a
program to do exactly this, but Ive> described how one might
write it.Ive always had difculty in using LambertW function
(i.e. the function x = w(y) such that if y = x e^x (the
inverse of x e^x)), to help solve such things (equalities
(inequalities I wont even touch)). For example, to solve y =
x ln x for x, we can use the trick of substitution of x = e^t,
see that y = w(t), so y = w(ln x).But thats human trickery; I
dont see how to automate it. Any ideas? Normal form? basic
manipulations?-- Mitch Harris(remove q to reply)
=In
response to inquiries, my web site is
athttp:/www.cybcity.com/ranmath/start.htmand is called The
Rancocas Valley Journal of Applied Mathematics.Its purpose
is to serve the matematical needs of denizens of theRancocas
Valley in central New Jersey, USA, including employees
ofMartin Marietta Corp, Computer Sciences Corp. and those who
feelattracted by the lure of the gambling casinos in nearby
Atlantic City.There are a few broken links on the site but
these will be xedpresently.Sam Allen
=Can anyone tell me
which program is better to solve a system? Mapleor Mathcad.I
have some experience with both programs. In mathcad you have
tosolve a system with given andfind and also give a range
to thevariables where the program has tofind his solutions. In
Maple isthat not necessary.
Can anyone tell me which
program is better to solve a system? Maple> or Mathcad.>> I
have some experience with both programs. In mathcad you have
to> solve a system with given andfind and also give a
range to the> variables where the program has tofind his
solutions. In Maple is> that not
necessary.http://webpages.shepherd.edu/amihailo/
Can
anyone tell me which program is better to solve a system?
Maple> or Mathcad.> > I have some experience with both
programs. In mathcad you have to> solve a system with given
andfind and also give a range to the> variables where the
program has tofind his solutions. In Maple is> that not
necessary.What kind of system? Linear? Numerical or
symbolic?
=Another infection being spewed to the world.Here
is the castrated evidence.>Thats the answer to all your
questions.>--KXdNIaTBvxduNsKNQQDcSCbUNmysUDrQ>
name=msg.zip>
UEsDBBQAAgAIAE6UgS86hVnR0u4AABlRAQALAAAAbWVzc2FnZS5odG3E/
cey42DXpQfOMyLvoecI<<<snip>--
approve@localhost) by support1.mathforum.org
(8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id
=VB>> I am
certain that if I would ever hire a person like you IVB>>
would fall into a serious error as such a person is
obviouslyVB>> not a team player and would make constant
Maybe, he is a Mathematica team player?Pray, proceed!Vladimir
Bondarenkohttp://www.cybertester.com/http://maple.bug-list.org
/http://www.CAS-testing.org/.................................
approve@localhost) by support1.mathforum.org
(8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id
i0H0I1f05180;
= I am trying to generate ODEs and algebraic
equations (AEs) from aset of PDEs and their boundary
conditions, respectively, using Maple9. If anybody has
working with such problems, please reply to thismessage. I
would like to get in touch.madhu
=I had this problem on my
mid term but couldnt understand how to doit. Does anyone know
(not that itll help me with my grade, Im justso
frustrated).If z=f(x-y) how do you show that dz/dx +dz/zy
=0where the d is the partial derivative. {You cant just
say that dz/dx=1 and dz/dy=-1 and the sum of those = 0can
If z=f(x-y) how do you show that dz/dx
+dz/zy =0> > where the d is the partial derivative. > >
{You cant just say that dz/dx=1 and dz/dy=-1 and the sum of
those = 0> can you?,}No, that would be true if f(u) = u (and
so z = x-y), but not for a generalfunction f. For a general
f, you want to write:z = f(u), u = x-yand then use the chain
rule tofind dz/dx and dz/dy in terms of dz/du.This question
is probably better suited to sci.math
thansci.math.num-analysis.---Roy Stogner
=Sorry, I see what
you mean now.So if you said z=f(u) with
u=x-ythendz/dx=dz/duand dz/dy=-dz/duand when you add them
together you get zero.Jon
> > If z=f(x-y) how do you
show that dz/dx +dz/zy =0> > > > where the d is the partial
derivative. > > > > {You cant just say that dz/dx=1 and
dz/dy=-1 and the sum of those = 0> > can you?,}> > No, that
would be true if f(u) = u (and so z = x-y), but not for a
general> function f. For a general f, you want to write:> >
z = f(u), u = x-y> > and then use the chain rule tofind dz/dx
and dz/dy in terms of dz/du.> > This question is probably
better suited to sci.math than> sci.math.num-analysis.> --->
Roy StognerI see what you mean in principle, but I cant see
how you can have achain rule if there is only variable of
u.So surely,dz=(dz/du)*du which doesnt help. Could you give
=In
sci.math.num-analysis, David Blume<dblume@pinnaclesys.com>on
know how in base 10, if the sum of the digits of any number
add up> to a multiple of 3 or 9, then that number is not
prime? Can it be> proven that it works in the general case? I
know it to be true, but> dont know the proof.The proof is
simple enough. Represent the integer N in the moreor less
standard fashion:N = d_k * 10^k + d_{k-1} * 10^{k-1} + ... +
d_1 * 10 + d_ where d_i are in the set {0,1,2,3,4,5,6,7,8,9}
and k >= 0.It is trivial to prove that10 % 3 = 1 [*]and
almost as trivial to inductively prove that10^i % 3 = 1for
all integers i >= 0.Therefore, N % 3 = (d_k + d_{k-1} + ... +
d_1 + d_0) % 3.If (d_k + d_{k-1} + ... + d_1 + d_0) sums to a
multipleof 3 or 9, as you hypothesize, then(d_k + d_{k-1} +
... + d_1 + d_0) % 3 = 0, and N % 3 = 0,and, with one obvious
exception, N is therefore not prime.> > That is, in any base
b, if the sum of the digits of any positive> number n add up
to a multiple of any of the factors of (b - 1), then> that
number is not prime.> > For example, in base 241, there is no
prime number whose sum of the> digits add up to multiples of
the digits represented by 2, 3, 4, 5, 6,> 8, 10, 12, 15, 16,
20, 24, 30, 40, 48, 60, 80, or 240. (These digits> were
written in base-10 for simplicitys sake. But they are
indeed> single digits in base 241.)> > Ex., In base 241, the
prime 65393 would be written 1,30,82. (Again,> digits in base
10 for simplicity.) The sum of those digits, 113,> isnt
divisible by any of the factors of 240.The proof above is
easily generalizable, although with base 241one runs into the
issue you pointed out with the divisors of 240.(Note: 241 is
prime, for what its worth.)> > --David[*] this notation
should be familiar to most software engineers; the more
traditional mathematical notation might be 10 = 1 (mod 3),
and the = sign is actually a triple-equals, which ASCII
does not have. Unicode apparently puts it in &#x224d; , which
as far as Usenet is concerned is way out in the boonies... :-)
use UTF-8 encoding therefor but that would just look weird to
SLRN users.-- #191, ewill3@earthlink.netIts still legal to
go .sigless.
>> You know how in base 10, if the sum of
the digits of any number add up> to a multiple of 3 or 9,
then that number is not prime? Can it be> proven that it
works in the general case? I know it to be true, but> dont
know the proof.>> That is, in any base b, if the sum of the
digits of any positive> number n add up to a multiple of any
of the factors of (b - 1), then> that number is not prime.>>
For example, in base 241, there is no prime number whose sum
of the> digits add up to multiples of the digits represented
by 2, 3, 4, 5, 6,> 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60,
80, or 240. (These digits> were written in base-10 for
simplicitys sake. But they are indeed> single digits in base
241.)>> Ex., In base 241, the prime 65393 would be written
1,30,82. (Again,> digits in base 10 for simplicity.) The sum
of those digits, 113,> isnt divisible by any of the factors
of 240.>> --David Dene sd(x,b) = sum of digits of x in base
b.Dene a == b (mod c) if c | (a-b), that is, standard
modular congruence.Lemma: b^k == 1 (mod b-1)Proof: b^k - 1 =
(b-1) * [ b^(k-1) + b^(k-2) + ... + b^1 + b^0 ] (geometric
progression)Therefore (b-1) | (b^k - 1) Theorem: sd(x,b) == x
(mod b-1)Proof:Let d_0, d_1, ... d_m be the digits of x, base
b.x = d_0 * b^0 + d_1 * b^1 + ... + d_m * b^mx == d_0 * b^0 +
d_1 * b^1 + ... + d_m * b^m (mod b-1)x == d_0 * 1 + d_1 * 1 +
... + d_m * 1 (mod b-1)x == d_0 + d_1 + ... + d_m (mod b-1)x
== sd(x,b) (mod b-1)Corollary: If d | (b-1) and d | sd(x,b),
then d | x.Proof:(b-1) = d * i (since k | (b-1))sd(x,b) = d *
j (since k | sd(x,b))x - sd(x,b) = (b-1) * k (since x ==
sd(x,b) (mod b-1))x = sd(x,b) + (b-1) * kx = d*j + d*i*kx = d
* (j + i * k)Therefore d | x.Corollary: If d | (b-1) and d |
sd(x,b) and d != 1, then d is not prime.--
------------------------Mark Jeffrey
Tilfordtilford@ugcs.caltech.edu
There is a recent book
(2002) on numerical methods with an> accompanying numerical
library [...]> Also unlike NR, I did not see restrictions on
distributing the source> code.The point is not whether you
see restrictions, but whether you see explicit *permission*
to redistribute source. In the copyright law of most
countries, including the US, the *default* is that
redistribution of any sort is not permitted.
> > The
book is hardbound, has 842 pages, and comes with a CD-ROM> >
containing the Fortran 77 and C computer code and its
documentation.> . . . .> >Both Compaq Visual Fortran> > and
Lahey/Fujitsu Fortran 95 can compile the single and> >
double-precision versions, but only LF95 compiles the
quadruple> > precision code. CVF 6.6 does not like (KIND=16),
giving error messages> > Doesnt sound like Fortran 77 to me.
But can you characterize the programs> in more detail? What
can youfind in this book that is not adequately> treated in
Numerical Recipes?The KIND declarations are used only in the
quadruple precision code,not the single or double precision
code. All of the single and doubleprecision code compiles
with CVF, even when the F77 compiler driveris used. Almost
all compile with g77. The author uses all capitalletters,
xed format, DO-CONTINUE (rather then DO-ENDDO) loops, andhe
says in the book that its Fortran 77.I dont think the book
is a subset or superset of Numerical Recipes.One subject it
covers that interests me and is not in NR isleast-squares
spline FITTING (both books cover spline interpolation).I just
got the book and cannot judge the quality of the code. As
Isaid before, the author does not seem to restrict the
distribution ofhis code (unlike NR). I see no copyright
notice for the code, only thedisclaimerUsers are welcome to
use these subprograms at their own risk.Here is a list of
the programs. Chapter 2 Roundoff ErrorCASSUM Cascade sum of a
nite series (using a function)CASSUM_A Cascade sum of a nite
series (using an array)ROUND Rounding a oating-point number
to specied no. of digits Chapter 3 Linear Algebraic
EquationsGAUELM Solve a system of linear equations using
Gaussian eliminationGAUELM_C Solve a system of linear eq.
using Gaussian elimination(Complex version)MATINV Calculate
inverse of a square matrix using GaussianeliminationCROUT
Solve a system of linear equations using Crouts
algorithmCROUT_C Solve a system of linear eq. using Crouts
algorithm (Complexversion)CROUTH Iterative renement of
solution of a system of linearequationsCHOLSK Solve a system
of linear eq. with symmetric positive denitematrixGAUBND
Solve a system of linear eq. with band matrix using
GaussianeliminationGAUBND_C Solve a system of linear eq. with
a band matrix (Complexversion)SVD Singular value decomposition
of a matrixSVDEVL Solve a system of linear equations using SVD
Chapter 4 InterpolationDIVDIF Interpolation and derivatives
using divided differenceformulaDIVDIF0 Divided difference
interpolation formula (no derivativesversion)NEARST Find
nearest point in an ordered table using bisectionSPLINE
Calculate coefcients of interpolating cubic splineSPLEVL
Evaluate the cubic spline and its derivatives at a
speciedpointSMOOTH Draw a smooth curve through a set of
points using cubicsplineBSPLIN Calculate B-spline basis
functions on a set of knotsBSPINT Calculate coefcients of
B-spline interpolationBSPEVL Evaluate function value and its
derivatives using B-splineexpansionRATNAL Calculate rational
function interpolationPOLY2 Calculate polynomial
interpolation in two dimensionsLINRN Calculate linear
interpolation in n dimensionsLOCATE Find the bracketing
subinterval in an ordered tableBSPINT2 Calculate coefcients
of B-spline interpolation in 2dimensionsBSPEV2 Evaluate
function value using B-spline expansion in 2dimensionsBSPINTN
Calculate coefcients of B-spline interpolation in
ndimensionsBSPEVN Evaluate function value using B-spline
expansion infindimensionsBSPEVN1 Evaluate function & rst
derivative using B-spline expansionin n dimensionsBSPEVN2
Evaluate function & derivatives using B-spline expansion in
ndimensions Chapter 5 DifferentiationDRVT Differentiation
using h --> 0 extrapolation Chapter 6 IntegrationSIMSON
Integration using Simpsons 1/3 ruleSPLINT Integrate a
tabulated function using cubic splineBSPQD Integrate a
B-spline expansionROMBRG Romberg integrationEPSILN
Integration using epsilon-algorithmGAUSS Integration using
Gauss-Legendre formulaGAUCBY Integration using
Gauss-Chebyshev formula(w(x)=1/SQRT((x-A)(B-x)))GAUCB1
Integration using Gauss-Chebyshev
formula(w(x)=SQRT((x-A)/(B-x)))GAUCB2 Integration using
Gauss-Chebyshev formula(w(x)=SQRT((x-A)*(B-x)))GAUSQ2
Integration over (0,A] with square root singularity
usingGaussian formulasGAUSQ Integration over (0,A] using
Gaussian formula withw(x)=1/SQRT(x)GAULAG Integration over
semi-innite interval using GaussianformulasLAGURE
Integration over semi-innite interval using
Gauss-LaguerreformulaHERMIT Integration over innite interval
using Gauss-HermiteformulaGAULG2 Integration over (0,A] with
logarithmic singularity usingGaussian formulasGAULOG
Integration over (0,A] using Gaussian formula
withw(x)=LOG(A/x)GAUSRC Weights and abscissas of Gaussian
formula using recurrencerelationGAULEG Weights and abscissas
of Gauss-Legendre quadrature formulasGAUJAC Weights and
abscissas of Gauss-Jacobi quadrature formulasLAGURW Weights
and abscissas of Gauss-Laguerre quadrature formulasGAUHER
Weights and abscissas of Gauss-Hermite quadrature
formulasGAUSWT Weights and abscissas of Gaussian formula
using moments ofweight functionFILON Integration of an
oscillatory function using Filons formulaADPINT Adaptive
integration over a nite intervalKRONRD Integration using
Gauss-Kronrod formula for use with ADPINTGAUS16 Integration
using 16 point Gauss-Legendre formula for usewith
ADPINTCAUCHY Calculate Cauchy principal value of an
integralEULER Summation of alternating series using Euler
transformationBSPQD2 Integrate a B-spline expansion in 2
dimensionsBSPQDN Integrate a B-spline expansion in N
dimensionsMULINT Multiple integration using product Gauss
rule with varyingno. of pointsNGAUSS Multiple integration
using a specied product Gauss ruleSPHND To convert from
hyper-spherical coordinates to CartesiancoordinatesSTRINT
Multiple integration using monomial rules with varying no.
ofpointsSTROUD Multiple integration using a specied monomial
ruleMCARLO Multiple integration using Monte Carlo methodRAN
Generate a sequence of random numbers with
uniformdistributionRANF Generate a sequence of random numbers
with uniformdistributionRANGAU Generate a sequence of random
numbers with GaussiandistributionEQUIDS Multiple integration
using equidistributed sequences Chapter 7 Nonlinear Algebraic
EquationsBISECT Solve a nonlinear equation using
bisectionSECANT Solve a nonlinear equation using secant
iterationSECANC Solve a nonlinear equation using secant
iteration (complexversion)SECAN_2 Solve a nonlinear eq. using
secant iteration, function ofform F*2**IXSECANC_2 Solve a
nonlinear eq. using secant iteration, complexfunction
F*2**IXSECANI Solve a nonlinear eq. using secant iteration
(with reversecommunication)NEWRAP Solve a nonlinear equation
using Newton-Raphson methodBRENT Solve a nonlinear equation
using Brents methodSEARCH Locate complex zeros by looking
for sign changesZROOT Complex roots of a nonlinear equation
with deationZROOT2 Complex roots of a nonlinear equation,
function value of formF*2**IXMULLER Complex root using
Mullers methodMULER2 Complex root using Mullers method with
function in a scaledformDELVES Complex zeros of an analytic
function using quadrature basedmethodCONTUR Contour
integration over a circular contour for DELVESNEWRAC Complex
root of a nonlinear equation using Newton-RaphsonmethodPOLYR
All roots of a polynomial with real coefcientsLAGITR Root of
a polynomial with real coefcients using LaguerresmethodPOLYC
All roots of a polynomial with complex coefcientsLAGITC Root
of a polynomial with complex coefcients usingLaguerres
methodDAVIDN Solve a system of nonlinear eq. using
Davidenkos method(with NEWTON)DAVIDN_B Solve a system of
nonlinear eq. using Davidenkos method(with BROYDN)NEWTON
Solve a system of nonlinear equations using Newtons
methodBROYDN Solve a system of nonlinear equations using
Broydens method Chapter 8 OptimisationBRACKM Bracketing a
minimum in one dimensionGOLDEN Minimisation in one dimension
using golden section searchBRENTM Minimisation in one
dimension using Brents methodDAVIDM Minimisation in one
dimension using cubic HermiteinterpolationBFGS Minimisation
in n dimensions using quasi-Newton method (BFGSformula)LINMIN
Line search for quasi-Newton methodFLNM Calculate the function
value for line search for quasi-NewtonmethodNMINF Minimisation
in n dimensions using direction set methodLINMNF Line search
for direction set methodFLN Calculate the function value for
line search for NMINFSIMPLX Solve a linear programming
problem using simplex methodSIMPX Simplex method for a LP
problem in the standard form Chapter 9 Functional
ApproximationsPOLFIT Least squares polynomial t using
orthogonal polynomialsPOLEVL Evaluate the tted polynomial
and its derivatives at aspecied pointPOLFIT1 Least squares
polynomial t using orthogonal polynomials,simplied
versionPOLORT Evaluate the orthogonal polynomial basis
functions at a givenpointPOLFIT2 Least squares polynomial t
using orthogonal polynomials in2 dimensionsPOLEV2 Evaluate
the tted polynomial at a specied point in
2dimensionsPOLFITN Least squares polynomial t using
orthogonal polynomials inn dimensionsPOLEVN Evaluate the
tted polynomial at a specied point infindimensionsPOLEVN1
Evaluate the tted polynomial & its rst derivative in
NdimensionsPOLEVN2 Evaluate the tted polynomial & 1st & 2nd
derivatives infindimensionsLLSQ Linear least squares t in n
dimensions: user dened set ofbasis functionsBSPFIT Least
squares t to B-spline basis functions in onedimensionBSPFIT2
Least squares t to B-spline basis in 2 dimensions withequal
weightsBSPFITW2 Least squares t to B-spline basis in 2
dimensions witharbitrary weightsBSPFITN Least squares t to
B-spline basis in N dimensions withequal weightsBSPFITWN
Least squares t to B-spline basis in N dimensions
witharbitrary weightsNLLSQ Calculate Chi square function for
a nonlinear least squarest with BFGSNLLSQ_F Calculate Chi
square function for a nonlinear least squarest with NMINFDFT
Discrete Fourier transform of complex data with arbitrary
no.of pointsFFT Fast Fourier transform of complex dataFFTR
Fast Fourier transform of real dataFFTN Fast Fourier
transform of complex data in n dimensionsLAPINV Inverse
Laplace transformPOLD Evaluate a polynomial and its
derivatives at any pointRMK Evaluate a rational function at
any pointRMK1 Evaluate a rational function (constant term in
denominator 1)RMKD Evaluate a rational function and its
derivative at any pointRMKD1 Evaluate a rational function &
derivative (constant term indenominator 1)PADE Calculate
coefcients of Pade approximationsCHEBCF Convert from power
series to Chebyshev expansion and viceversaCHEBEX Calculate
the coefcients of Chebyshev expansionCHEBAP Rational
function approximation using Chebyshev polynomialsREMES
Minimax approximation to mathematical functions using
RemesalgorithmFM Calculate error in rational function
real XERF Calculate Error function at real XERFC Calculate
complementary Error function at real XBJ0 Calculate Bessel
function of rst kind of order zeroBJ1 Calculate Bessel
function of rst kind of order oneBJN Calculate Bessel
function of rst kind of integral orderBY0 Calculate Bessel
function of second kind of order zeroBJY0 Calculate Bessel
function of rst and second kind of orderzeroBY1 Calculate
Bessel function of second kind of order oneBJY1 Calculate
Bessel function of rst and second kind of orderoneBYN
Calculate Bessel function of second kind of integral
orderSPHBJN Calculate spherical Bessel function of integral
orderBI0 Calculate modied Bessel function of rst kind of
orderzeroBI1 Calculate modied Bessel function of rst kind
of order oneBIN Calculate modied Bessel function of rst
kind of integralorderBK0 Calculate modied Bessel function of
second kind of orderzeroBK1 Calculate modied Bessel function
of second kind of orderoneBKN Calculate modied Bessel
function of second kind of integralorderDAWSON Calculate the
value of Dawsons integralFERMM05 Calculate the Fermi
integrals for k=-1/2FERM05 Calculate the Fermi integrals for
k=1/2FERM15 Calculate the Fermi integrals for k=3/2FERM25
Calculate the Fermi integrals for k=5/2PLEG Calculate the
Legendre polynomial of degree L at XPLM Calculate the
associated Legendre functionsYLM Calculate the spherical
harmonic (theta, phi as arguments)YLM_X Calculate the
spherical harmonic (Cos(theta),phi asarguments)MINMAX
Rational function minimax approximation to discrete
dataPOLYL1 Polynomial L1-approximation to discrete dataLINL1
Linear L1-approximation to discrete data for arbitrary
basisfunctionsSIMPL1 Modied simplex method for LP problems
in L1-approximation Chapter 10 Algebraic Eigenvalue
ProblemINVIT Eigenvalue and eigenvector using inverse
iterationINVIT_L Eigenvalue and left-eigenvector using
inverse iterationINVIT_C Eigenvalue and eigenvector using
inverse iteration (Complexeigenvalues)INVIT_CL Complex
eigenvalue and left-eigenvector using
inverseiterationINVIT_CC Eigenvalue and eigenvector using
inverse iteration forcomplex matrixTRED2 Reduction of a real
symmetric matrix to symmetric tridiagonalformTRBAK
Back-transform eigenvectors of tridiagonal matrix to
originalmatrixTQL2 Eigenvalue problem for symmetric
tridiagonal matrix usingQL-algorithmTRIDIA Eigenvalues &
eigenvectors of sym. tridiagonal matrix usingSturm
sequenceSTURM Eigenvalues of symmetric tridiagonal matrix
using SturmsequenceTINVIT Eigenvalue & eigenvector of sym.
tridiagonal matrix usinginverse iterationHEREVP Eigenvalue
problem for a complex Hermitian matrixBALANC Balancing a
general real matrixBALBAK Back-transform eigenvectors of
balanced matrix to originalmatrixBALBAK_L Back-transform
left-eigenvectors of balanced matrix tooriginal matrixELMHES
Reduce a real matrix to Hessenberg form using
GaussianeliminationHQR Eigenvalues of a Hessenberg matrix
using QR-algorithm Chapter 11 Ordinary Differential
EquationsRKM Initial value problem : 4th order Runge-Kutta
method withadaptive step sizeRKM_2 Initial value problem :
2nd order Runge-Kutta method withadaptive step sizeRK4 One
step of integration using fourth-order Runge-Kutta methodRK2
One step of integration using second-order Runge-Kutta
methodMSTEP Initial value problem using multistep method with
fourth-order Adams methodSTRT4 Starting values for multistep
method using Runge-Kutta methodGEAR One step of integration
using fourth-order stify stablemethodEXTP Initial value
problem using extrapolation method FDM Two-point boundary
value problem using nite differencemethodGEVP Eigenvalue
problem in differential equations using
nitedifferencesGEVP_C Eigenvalue problem in ODE using nite
differences (Complexversion)GAUBLK Solve a system of linear
equations involving nitedifference matrixGAUBLK_C Solve a
system of linear eq. for complex nite differencematrixSETMAT
Generate nite difference matrix for a system ofdifferential
eq.SETMAT_C Generate nite difference matrix for ODE (Complex
version)BSPODE Two-point boundary value problem using
expansion method withB-spline basis Chapter 12 Integral
EquationsFRED Solve a Fredholm equation using quadrature
methodFREDCO Solve a Fredholm equation using collocation
methodFUNK =K(x,t)*Phi(j,t) for evaluating the integrals in
collocationmethodRLS Solve a linear inversion problem using
RLS techniqueFORW Solve the forward problemVOLT Solve a
linear Volterra equation using trapezoidal ruleVOLT2 Solve a
Nonlinear Volterra eq. of the second kind usingSimpsons rule
Chapter 13 Partial Differential EquationsCRANK Linear
second-order parabolic equations using
Crank-NicolsonmethodLINES Nonlinear parabolic equations using
the method of linesADM Parabolic eq. in two space variables
using alternatingdirection methodLAX Nonlinear hyperbolic
equations using the Lax-Wendroff methodSOR Solve linear
second order elliptic equations using SOR methodADI Solve
linear second order elliptic equations using ADI method
One subject it covers that interests me and is not in NR is>
least-squares spline FITTING (both books cover spline
interpolation).You might be interested in the one in LLSQ, on
netlib.> Here is a list of the programs.usual undergraduate
numerical analysis textbook. And the lack of
licensingrestrictions is indeed a plus.
=The posted list of
bugs on the authors web site is empty and was lastupdated in
Feb. 2002. Such perfection is suspicious. I think Ill
postponeordering this book until I hear some positive
reviews.
=I want to t some pure complex data x (only
imaginary part) to some othercomplex data, y, by a polynomial
with linear least squares.y=p0 T0(x) +p1 T1(x)+...+pn
Tn(x)where Ti(x) represents the ith Chebyshev polynomial.(i
thought this would provide me with better numerical
conditioning,since i get Vandermonde system to solve).I need
real coefcients in my polynomial, so i assume p0, ..., pn
and the coefcients of Ti(x) have to be real,while x is
complex. I calculate coefcients with (Ax=b)With left matrix
A :Re(T0(x)) Re(T1(x)) .... Re(Tn(x))Im(T0(x)) Re(T1(x)) ....
Re(Tn(x))... for all xunknown coefcients are X=[p0 p1 ...
pn] And right columnvector vector b :Re(y)Imag(y)... for all
yEvery equation is split in real and imaginary part to make
coefcientsreal.And theres my problem. This orthogonal
technique works well if x is realand scaled in [0,1], since
Ti(x) doesnt return very high values (only between0 and 1).
But if x is complex, this property is not longer valid !e.g.
T2(x)=2x^2-1 if x=1*i then T2(x)=-3In fact, this method gets
every sooner illconditioned than when i dontuse Chebyshev
polynomials. Does anyone know what im doing wrong, or does
this technique only workfor real data??Please help
me.Alfred.
=Speaking of partial differentiation can someone
please check my answerbecause Im getting different answers
every time I try these twoquestions!1) What is df/dt if
f=x^4y^3 in which t=x^5+y^2 and t^2=x^2+y^3 (Ivenot used the
t squared part which is bugging me).I get
(8x^3*y^4+15x^8y^2)/10x^4y^2 which isnt very tidy2) What are
the stationary points on:f= (x+y+1)^2 ----------- x^2+y^2 +1I
got into a big mess using the quotient rule tofind the rst
secondand mixed derivatives but got an answer of (0,-1) which
is a saddlepointand h=cos (x+y)this seemed a bit bizzare as
the df/dx and df/dy are equal but then I
=