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We use the standard multiple shooting method to solve a linear two pointboundary-value problem. To ensure that the solution obtained by combining thepartial solutions is continuous and satisfies the boundary conditions, we haveto solve a system of linear equations. Our idea is to first solve a bidiagonalsystem related to the original system of linear equations, and then update itwith the Sherman-Morrison-Woodbury formula. We study the feasibility, thenumerical stability and the running time of this method. The results are: Themethod described above has the same stability problems like the well knownCondensing method. The running time analysis shows that the new method isslower than the Condensing method. Therefore we recommend not to use the methoddescribed in this article.

Using the Sherman-Morrison-Woodbury Formula to Solve the System of  Linear Equations from the Standard Multiple Shooting Method for a Linear Two  Point Boundary-Value Problem is a Bad Idea