Based on QR-like decomposition with column pivoting, a new and efficient numerical method for solving symmetric matrix inverse eigenvalue problems is proposed, which is suitable for both the distinct and multiple eigenvalue cases. A locally quadratic convergence analysis is given. Some numerical experiments are presented to illustrate our results. Key words: inverse eigenvalue problems, QR-like decomposition, least squares, Gauss-Newton method AMS(MOS) subject classification: 65F15, 65H15 1 This research was supported in part by the National Natural Science Foundation of China and the Jiangsu Province Natural Science Foundation. The work of the author was done during a visit to CERFACS, France in March-August 1998. 1. Introduction Let A(c) be the affine family A(c) = A 0 + n X i=1 c i A i (1) where A 0 ; A 1 ; \Delta \Delta \Delta ; A n are real symmetric n \Theta n matrices, and c = (c 1 ; \Delta \Delta \Delta ; c n ) T 2 R n . We consider inverse eigenvalue problems(IE...