Two new algorithms based on QR decompositions (QRDs) (with column pivoting) are proposed for solving inverse eigenvalue problems, and under some non-singularity assumptions they are both locally quadratically convergent.
Several numerical tests are presented to illustrate their convergence behavior.  

As a continuation of [1], this paper considers implementation of ODE approaches. A modified Hamming's algorithm for integration of (ECP)-equation is suggested to obtain a local solution. In addition to the main algorithm, three supporting algorithms are also described: two are for evaluation of the right-hand side of (ECP)-equation, which may be especially suitable for certain kinds of (ECP)-equation when applied to large scale problems; the third one, with a convergence theorem, is for computing an initial feasible point. Our numerical results obtained by executing these algorithms on an example of (ECP)-equation given in [1] on five test problems indicate their remarkable superiority of performance to Tanabe's ODE version that is recently claimed to be much better than some well-known SQP techniques.  

A spline collocation method is proposed to approximate the periodic solution of nonlinear ordinary differential equations. It is proved that the cubic periodic spline collocation solution has the same error bound $O(h^4)$ and superconvergence of the derivative at collocation points as that of the interpolating spline function. Finally a numerical example is given to demonstrate the effectiveness of our algorithm.

A class of implicit trapezoidal TVD schemes is proven to satisfy a discrete convex entropy inequality and the solution sequence of such implicit trapezoidal schemes converges to the physically relevant solution for genuinely nonlinear scalar conservation laws. The results are extended for a class of generalized implicit one-leg TVD schemes.

In this paper, the stability of biquadratic-bilinear velocity-pressure finite elements are discussed for the stationary Stokes problem. It is proved that there exist constants $c ,c' ＞0$ independent of $h$ such that

 
Hence a question in [1] is answered.

With the help of Brouwer's fixed point theorem and the relations of the eigenvalues and diagonal elements of a Hermitian matrix, we give some new sufficient conditions for the solubility of algebraic inverse eigenvalue problems.

The continuity conclusions about rational Hermite interpolating functions are given under some conditions. On that basis, we establish the convergence results for the paradiagonal sequences of the rational interpolants for Stieltjes functions and Hamburger functions.