A more interesting use of Padé approximation is “two-point Padé approximation” or Padé interpolation in which a Padé approximant for f(x) is constructed from two truncated Taylor series: one for when x is very small and one is for when x is very large. The Padé approximant in this method interpolates between the values at which f(x) is known. This method is directly applicable to perturbation t...

This paper proposes an approach to algorithmically synthesize control strategies for discrete-time nonlinear uncertain systems based on reachable set computations using the ellipsoidal calculus. For given ellipsoidal initial sets and bounded ellipsoidal disturbances, the proposed algorithm iterates over conservatively approximating and LMI-constrained optimization problems to compute stabilizin...

The Potential Energy Surface PES of (H2)2 dimer has been investigated, using five simple rigid rotor models. These models are called: head to head, symmetric side to side, L , steplike and T model. All calculations were done at two levels of ab initio  methods: MP2(Full) and QCISD (T,Full) using cc-pVTZ basis set at singlet state of spin multiplicity. The results of scanning PES were then fitte...

This paper preliminarily reports an SMT for solving polynomial inequalities over real numbers. Our approach is a combination of interval arithmetic (over-approximation, aiming to decide unsatisfiability) and testing (under-approximation, aiming to decide Satisfiability) to sandwich precise results. Addition to existing interval arithmetic’s, such as classical intervals and affine intervals, we ...

An approximation of function u(x) as a Taylor series expansion about a point x0 at M points xi , ∼i = 1, 2, . . . ,M is used where xi are arbitrary-spaced. This approximation is a linear system for the derivatives u with an arbitrary accuracy. An analytical expression for the inverse matrix A−1 where A = [Aik] = 1 k! (xi − x0) is found. A finite-difference approximation of derivatives u of a gi...

In recent years, the Takagi–Sugeno (T–S) fuzzy model has been commonly used for the approximation of nonlinear systems. Using the T-S fuzzy model, nonlinear systems can be converted into linear time-varying systems, which can reduce approximation errors compared with the conventional Taylor approximation. In this paper, we propose a new nonlinear filter with a finite impulse response (FIR) stru...

In this paper, the first and second order approximations of Taylor expansion are used for calculating the change of each natural frequency by modifying an arbitrary parameter of a system with a known amount and based on this approximation, the inverse eigenvalue problem is transformed to a solvable algebraic equation. The finite element formulation, based on the classical laminated plate theory...

We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finitedimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the recently-proposed random Fourier features [Rahimi and Recht, 2007] in terms of the number of features, we show how this polynomial representation can provide a be...

Let A be the generator of an n-times integrated semigroup T (·) and let r ∈ N. We first prove the equivalence of Riemann, Peano, and Taylor operators, which are three different expressions of the r-th power of A1, the part of A in the closure of the domain D(A) of A. Then we discuss optimal and non-optimal rates of approximation of T (·)x for x ∈ D(Ar−1 1 ), via the (n + r)-th Taylor expansion ...

In this letter, we propose a simple but effective technique that improves statistical model-based voice activity detection (VAD) by both reducing computational complexity and increasing detection accuracy. The improvements are made by applying Taylor series approximations to the exponential and logarithmic functions in the VAD algorithm based on an in-depth analysis of the algorithm. Experiment...