Minimum Condition Number Research Articles

On the structure of a table of multivariate rational interpolants

In the table of multivariate rational interpolants the entries are arranged such that the row index indicates the number of numerator coefficients and the column index the number of denominator coefficients. If the homogeneous system of linear equations defining the denominator coefficients has maximal rank, then the rational interpolant can be represented as a quotient of determinants. If this system has a rank deficiency, then we identify the rational interpolant with another element from the table using less interpolation conditions for its computation and we describe the effect this dependence of interpolation conditions has on the structure of the table of multivariate rational interpolants. In the univariate case the table of solutions to the rational interpolation problem is composed of triangles of so-called minimal solutions, having minimal degree in numerator and denominator and using a minimal number of interpolation conditions to determine the solution.

Relations between block relative gain and Euclidean condition number

New relations between the block relative gain and condition number as well as the minimal condition number are developed. The results obtained show that the condition number must be large if the corresponding block relative gain has a large maximum singular value, and the minimal condition number must be large if the block relative gain has a large structured single value. These relations improve the previous result of C.N. Nett and V. Manousiouthakis (1987) and are useful in clarifying the role of block relative gain as a measure of potential design difficulties associated with plants that have large block relative gains. >

スカラロボットの絶対位置決め精度の補正

This paper presents a new kinematic calibration method based on condition number and an error map method for SCARA robots. The geometric parameters can be identified more precisely by measuring the positions of a hand with minimum condition number configuration. Furthermore, the error map method improves the accuracy of geometric parameters. The experimental results demonstrate that the calibration method made the maximum absolute positioning error of a typical SCARA DD robot less than 0.25mm all over the working area, while the maximum error was 2.20mm in the case of the conventional method.

Kinematic Calibration of SCARA Robot with Condition Number and Error Map Method

Summary This paper presents a new kinematic calibration method based on condition number and an error map method for SCARA robots. The geometric parameters can be identified more precisely by measuring the positions of a hand with minimum condition number configuration. Furthermore, the error map method improves the accuracy of geometric parameters. The experimental results demonstrate that this calibration method made the maximum absolute positioning error of a typical SCARA DD robot less than 0.25 mm all over the working area, while the maximum error was 2.20 mm in the case of the conventional method.

Block scaling with optimal Euclidean condition

Let M denote the set of all complex n × n matrices whose columns span certain given linear subspaces. The minimal Euclidean condition number of matrices in M is given in terms of the canonical angles between the linear subspaces, and optimal matrices in M are described. The result is also stated in terms of norms of certain projections.

A measure for Ill-conditioning of matrices in interval arithmetic

The new condition numberV(A) is proposed. This condition number measures ill-conditioning in interval arithmetic. The reliability of the condition numberV(A) has been proved. It is shown that Bauer's minimum condition number [2] and the condition numberV(A) are essentially equivalent although different approaches were used to derive them.

On the condition number of local bases for piecewise cubic polynomials

The condition number of the Gram matrix associated with piecewise polynomial finite element bases is discussed in general, and computed explicitly for cubic splines and cubic Hermite polynomials. In the latter case, we discuss the inherent ambiguity in the basis, and find the minimum condition number.

Matrices which can be optimally scaled

Sufficient conditions are given for a matrix to be optimally scalable in the sense of minimizing its condition number. In particular, in the case of simultaneous row- and column-scaling and subordinate to thel 1- orl ?-norm the minimal condition number is achieved for fully indecomposable matrices.