Verilog HDL: Magnitude
For a vector (a,b), the magnitude representation is the following:
A common approach to implementing these arithmetic functions is to use the Coordinate Rotation Digital Computer (CORDIC) algorithm. The CORDIC algorithm calculates the trigonometric functions of sine, cosine, magnitude, and phase using an iterative process. It is made up of a series of micro-rotations of the vector by a set of predetermined constants, which are powers of two. Using binary arithmetic, this algorithm essentially replaces multipliers with shift and add operations. In a Stratix™ device, it is possible to calculate some of these arithmetic functions directly, without having to implement the CORDIC algorithm.
In recent years large scientific interest has been
devoted to joint data decoding and parameter estimation
techniques. In this paper, iterative turbo decoding joint
to channel frequency and phase estimation is proposed.
The phase and frequency estimator is embedded into the
structure of the turbo decoder itself, taking into consideration
both turbo interleaving and puncturing. Results
show that the proposed technique outperforms conventional
approaches both in terms of detection capabilities and
implementation complexity.
LSVMK Langrangian Support Vector Machine algorithm
LSVMK solves a support vector machine problem using an iterative
algorithm inspired by an augmented Lagrangian formulation.
This standard describes a keyed-hash message authentication code (HMAC), a
mechanism for message authentication using cryptographic hash functions. HMAC can
be used with any iterative Approved cryptographic hash function, in combination with a
shared secret key. The cryptographic strength of HMAC depends on the properties of the
underlying hash function. The HMAC specification in this standard is a generalization of
Internet RFC 2104, HMAC, Keyed-Hashing for Message Authentication, and ANSI
X9.71, Keyed Hash Message Authentication Code.
迭代自適應Simpson，Lobatto積分
In almost every standard book on numerics quadrature algorithms like the adaptive Simpson or the adaptive Lobatto algorithm are presented in a recursive way. The benefit of the recursive programming is the compact and clear representation. However, recursive quadrature algorithms might be transformed into iterative quadrature algorithms without major modifications in the structure of the algorithm.
We present iterative adaptive quadrature algorithm (adaptiveSimpson and adaptiveLobatto), which preserves the compactness and the clarity of the recursive algorithms (e.g. quad, quadv, and quadl). Our iterative algorithm provides a parallel calculation of the integration function, which leads to tremendous gain in run-time, in general. Our results suggest a general iterative and not a recursive implementation of adaptive quadrature formulas, once the programming language permits parallel access to the integration function. For details the attached PDF file Conrad_08.pdf.
Generating Fractals with SSE/SSE2
You probably have heard about fractals before. They are beautiful pictures such as the one shown above. Any fractal can be described using iterative formulas. So you can generate a fractal by evaluating these formulas and finding the color of each pixel. That is a large computational task, and drawing a fractal needs a fast CPU and a carefully optimized program.
SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written in C and is callable from either C or Fortran. The library routines will perform an LU decomposition with partial pivoting and triangular system solves through forward and back substitution. The LU factorization routines can handle non-square matrices but the triangular solves are performed only for square matrices. The matrix columns may be preordered (before factorization) either through library or user supplied routines. This preordering for sparsity is completely separate from the factorization. Working precision iterative refinement subroutines are provided for improved backward stability. Routines are also provided to equilibrate the system, estimate the condition number, calculate the relative backward error, and estimate error bounds for the refined solutions.
observable distribution grid are investigated. A distribution
grid is observable if the state of the grid can be fully determined.
For the simulations, the modified 34-bus IEEE test feeder is used.
The measurements needed for the state estimation are generated
by the ladder iterative technique. Two methods for the state
estimation are analyzed: Weighted Least Squares and Extended
Kalman Filter. Both estimators try to find the most probable
state based on the available measurements. The result is that
the Kalman filter mostly needs less iterations and calculation
time. The disadvantage of the Kalman filter is that it needs some
foreknowlegde about the state.
