We present an algorithm that on input of an n×n symmetric diagonally dominant matrix A with m non-zero entries constructs in time Õ(m log n) a solver which on input of a vector b computes a vector x satisfying ||x−Ab||A < �||Ab||A in time Õ(m log n log(1/�)) 1. The new algorithm exploits previously unknown structural properties of the output of the incremental sparsification algorithm given in ...

an indirect tarns-log production function was employed to estimate the demand functions for such inputs as: fertilizer, seed, pesticide, water recourse and machinery as subject to budget constraint and while using data related to cotton producers in the three provinces of north khorasan, khorasane razavi, and south khorasan in 2007-8. lagrange coefficients with relation to cotton producers in t...

We give space-efficient geometric algorithms for three related problems. Given a set of n axis-aligned rectangles in the plane, we calculate the area covered by the union of these rectangles (Klee’s measure problem) in O(n log n) time with O( √ n) extra space. If the input can be destroyed and there are no degenerate cases and input coordinates are all integers, we can solve Klee’s measure prob...

We consider the NP-complete problem of deciding whether an input graph on n vertices has k vertex-disjoint copies of a fixed graph H . For H = K3 (the triangle) we give an O(2 2k log n) algorithm, and for general H an O(2k|H| log k+2k|H| log |H|n|H|) algorithm. We introduce a preprocessing (kernelization) technique based on crown decompositions of an auxiliary graph. For H = K3 this leads to a ...

Numerical integration methods are used to find the numerical solution of the transient analysis of electrical circuits. Because the electrical circuits are modelled by stiff differential algebraic equations, the BDF-methods are very popular in circuit simulation. Error control is used to handle with the trade-off between efficiency and accuracy. For optimization purposes smooth behaviour of the...

The log-aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. However, their input method proposed so far by use of three soc...

A randomized algorithm A can be thought of as a function A : {0, 1} n × {0, 1} R(n) → {Accept, Reject}, that is, function A is a deterministic algorithm that takes two input strings x and y, where x is the " real " input to the randomized algorithm and y is the random string used during the computation. Definition 1 A (deterministic) function G : {0, 1} m → {0, 1} R(n) is a pseudorandom generat...

The fragile complexity of a comparison-based algorithm is f(n) if each input element participates in O(f(n)) comparisons. In this paper, we explore the algorithms adaptive to various restrictions on input, i.e., with parameterized by quantity other than size n. We show that searching for predecessor sorted array has \(\varTheta (\log k)\), where k rank query element, both randomized and determi...