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A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

For a catastrophically unstable recurrence in one direction, any seed values for consecutive x_j and x_(j+1) will converge to the desired sequence of functions in the ...

Numerical stability refers to how a malformed input affects the execution of an algorithm. In a numerically stable algorithm, errors in the input lessen in significance as ...

A fixed point for which the eigenvalues are complex conjugates.

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

The best known example of an Anosov diffeomorphism. It is given by the transformation [x_(n+1); y_(n+1)]=[1 1; 1 2][x_n; y_n], (1) where x_(n+1) and y_(n+1) are computed mod ...

Let f:R×R->R be a one-parameter family of C^2 map satisfying f(0,0)=0 [(partialf)/(partialx)]_(mu=0,x=0)=0 [(partial^2f)/(partialx^2)]_(mu=0,x=0)>0 ...

A method for finding a matrix inverse. To apply Gauss-Jordan elimination, operate on a matrix [A I]=[a_(11) ... a_(1n) 1 0 ... 0; a_(21) ... a_(2n) 0 1 ... 0; | ... | | | ... ...

Jessen's orthogonal icosahedron is a concave shaky polyhedron constructed by replacing six pairs of adjacent triangles in an icosahedron (whose edges form a skew ...