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I want to solve the usual $A x = b$ system, where

$$A = \begin{bmatrix} B & c \\ c^{T} & 0 \end{bmatrix}$$

where $B \in \mathbb{R}^{n \times n} $ is a positive definite matrix, and $c \in \mathbb{R}^{n}$. Matrix $A$ is neither positive definite nor positive semidefinite.

I am not aware of well-known methods such as Cholesky or $LDL^T$ to solve this. Is there an efficient method to tackle this problem?

I want to solve the usual $A x = b$ system. In block form:

$$ \begin{bmatrix} B & c \\ c^{T} & 0 \end{bmatrix} \begin{bmatrix} x' \\ x_{n+1} \end{bmatrix} = \begin{bmatrix} b' \\ b_{n+1} \end{bmatrix}$$

where

• $B \in \mathbb{R}^{n \times n} $ is a positive definite matrix
• $c \in \mathbb{R}^{n}$
• $x,b \in \mathbb{R}^{n+1}$, so $x',b' \in \mathbb{R}^{n}$ and $x_{n+1},b_{n+1} \in \mathbb{R}$

Matrix $A$ is neither positive definite nor positive semidefinite.

I am not aware of well-known methods such as Cholesky or $LDL^T$ to solve this. Is there an efficient method to tackle this problem?

I want to solve the usual $A x = b$ system, where

$$A = \begin{bmatrix} B & e \\ e^{t} & 0 \end{bmatrix}$$

where matrix $B \in \mathbb{R}^{n \times n} $ is positive definite, and $e \in \mathbb{R}^{n}$. Matrix $A$ is neither positive definite nor positive semidefinite.

I am not aware of well-known methods such as Cholesky or $LDL^T$ to solve this. Is there an efficient method to tackle this problem?

I want to solve the usual $A x = b$ system, where

$$A = \begin{bmatrix} B & c \\ c^{T} & 0 \end{bmatrix}$$

where $B \in \mathbb{R}^{n \times n} $ is a positive definite matrix, and $c \in \mathbb{R}^{n}$. Matrix $A$ is neither positive definite nor positive semidefinite.

I am not aware of well-known methods such as Cholesky or $LDL^T$ to solve this. Is there an efficient method to tackle this problem?

I want to solve the usual $A x = b$ system. The matrix A is composed as follows: $$ \begin{bmatrix} B & e \\ e^{t} & 0\\ \end{bmatrix} $$

where $B \in \mathbb{R}^{n \times n} $ is a positive definite matrix, $e \in \mathbb{R}^{n}$.

The matrix A is not positive definite or positive-semidefinite, so i am not aware of well-known methods such as Cholesky or $LDL^T$ to solve this.

  Is there an efficient method to tackle this problem?

I want to solve the usual $A x = b$ system, where

$$A = \begin{bmatrix} B & e \\ e^{t} & 0 \end{bmatrix}$$

where matrix $B \in \mathbb{R}^{n \times n} $ is positive definite, and $e \in \mathbb{R}^{n}$. Matrix $A$ is neither positive definite nor positive semidefinite.

I am not aware of well-known methods such as Cholesky or $LDL^T$ to solve this. Is there an efficient method to tackle this problem?