Previously, we have discussed a recursive solution to the vector normal equation utilizing the recursive Cholesky and Modified Gram-Schmidt Orthogonalization (MGSO) algorithms. Previously, we have also discussed a blind adaptive approach for detection and extraction of signals of interest in the presence of noise and interference without relying on preamble or training sequences. The heart of t...

We provide a review of different approaches to linking model structure to observed behavior with a particular view towards using models for theory building. We identify four such approaches, namely the " classical " approach, the " pathway participation " approach, the " eigenvalue elasticity " approach, and the " eigenvector " approach, respectively. We outline our assessment of the strengths ...

A classical result due to Bochner characterizes the classical orthogonal polynomial systems as solutions of a secondorder eigenvalue equation. We extend Bochner’s result by dropping the assumption that the first element of the orthogonal polynomial sequence be a constant. This approach gives rise to new families of complete orthogonal polynomial systems that arise as solutions of second-order e...

Come with us to read a new book that is coming recently. Yeah, this is a new coming book that many people really want to read will you be one of them? Of course, you should be. It will not make you feel so hard to enjoy your life. Even some people think that reading is a hard to do, you must be sure that you can do it. Hard will be felt when you have no ideas about what kind of book to read. Or...

Fixed-Polynomial Approximate Spectral Transformations for Preconditioning the Eigenvalue Problem by Heidi K. Thornquist Arnoldi’s method is often used to compute a few eigenvalues and eigenvectors of large, sparse matrices. When the eigenvalues of interest are not dominant or wellseparated, this method may suffer from slow convergence. Spectral transformations are a common acceleration techniqu...

We present a uniied approach to subdivision algorithms for meshes of arbitrary topology admitting a rigorous analysis of the generated limit surfaces. A generalized suucient criterion for generating tangent plane continuous surfaces is provided. In particular, it applies to complex eigenvalues and also shows that the so-called double dominant eigenvalue condition, which was supposed to be indis...

This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input nodes in order to guarantee consensus of networks with negative edges as well as maximizing the convergence rate of distributed systems. We develop a submodul...