Jacobi Definition and 60 Threads

  1. G

    Jacobi Iteration Homework: Solving System of Equations

    Homework Statement consider the systems of equations 2x1 - x2 = 1 -31 + 4x2 =11 a) determine the ixact solution? b)apply jacobi iteration.Does the matrix C satisfy the required condition? c)starting with x(0) =( \stackrel{1}{1} ) calculate x(1) and x(2) and the prior error bound for x(2)...
  2. K

    What is the Proof for the Jacobi Symbol Property (ii)?

    This is a theorem about Jacobi symbols in my textbook: Let n and m be ODD and positive. Then (a/nm)=(a/n)(a/m) and (ab/n)=(a/n)(b/n) Moreover, (i) If gcd(a,n)=1, then (a^2/n) = 1 = (a/n^2) (ii) If gcd(ab,nm)=1, then (ab^2/nm^2)=(a/n) ===================================== (i) is easy and...
  3. S

    Geodesic deviation & Jacobi Equation

    http://en.wikipedia.org/wiki/Jacobi_field also see http://iopscience.iop.org/0305-4470/14/9/029/?ejredirect=.iopscience What's the difference between the jacobi equation and the geodesic deviation equation?
  4. D

    Solving Jacobi Matrices: Finding Det H6

    Homework Statement An n x n array Hn = (hij) is said to be a jacobi matrix if hij = 0 whenever |i - j| >= 2. Suppose Hn also has the property that for each index i, hii = a, hi, i+1 = b and hi,i-1 = c. For instance, H4 = a b 0 0 c a b 0 0 c a b 0 0 c a (i) Show that det Hn = a (det Hn-1) -...
  5. A

    What are Jacobi coordinates, and why are they useful?

    What are "Jacobi coordinates," and why are they useful? I am working on a quantum chemistry problem involving triatomic molecules. My advisor keeps talking about "Jacobi coordinates" and how they're a calculational convenience when it comes time to write out the Hamiltonian. Can someone...
  6. R

    Jacobi Method; Simple system of equations

    I know this is simple, and I am missing something obvious. I'm suposed to use the "jacobi method"; and with each iteration it should be getting closer and closer to the solution (x=2 and y=1, which it is not). Could someone explain what I'm doing wrong, or how to start...
  7. S

    How Do Jacobi Elliptic Functions Model Pendulum Motion?

    [Solved] Jacobi Elliptic Equations Homework Statement -t + \frac{P(\alpha)}{4} = \sqrt{\frac{l}{g}}\int\frac{ds}{\sqrt{1-k^{2}sin^{2}s}} = \sqrt{\frac{l}{g}}F(k, \phi). It is integrated from 0 to \phi For fixed k, F(k, \phi) has an "inverse," denoted by sn(k, u), that satisfies u =...
  8. P

    Binary Jacobi Symbol Algorithm: Add, Subtract & Shift

    Jacobi Symbol - Binary NOTE: if its past 8:30 AM Eastern Time, don't worry about it. thanks for the consideration The Question: Exercise 13.1. Develop a “binary” Jacobi symbol algorithm, that is, one that uses only addition, subtractions, and “shift” operations, analogous to the binary...
  9. E

    How Does the Hamilton-Jacobi Equation Reveal Solutions Depending on Potential V?

    Let be the S function being the action in physics S=S(x,y,z,t) satisfying the equation: \frac{dS}{dt}+(1/2m)(\nabla{S})^{2}+V(x,y,z,t)=0 where V is the potential is there any solution (exact) to it depending on V?
  10. E

    Strange Hamilton Jacobi equation

    let be (dS/dt)+(gra(S))^2/2m+(LS)+V(x) where L is the Laplacian Operator and V is the potential...could it be considered as the Hamiltan Jacobi equation for a particle under a potential Vtotal=V(x)+(LS) where S is the action
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