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diff --git a/src/main/java/org/apache/commons/math3/linear/JacobiPreconditioner.java b/src/main/java/org/apache/commons/math3/linear/JacobiPreconditioner.java
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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.linear;
+
+import org.apache.commons.math3.analysis.function.Sqrt;
+import org.apache.commons.math3.util.MathArrays;
+
+/**
+ * This class implements the standard Jacobi (diagonal) preconditioner. For a matrix A<sub>ij</sub>,
+ * this preconditioner is M = diag(1 / A<sub>11</sub>, 1 / A<sub>22</sub>, &hellip;).
+ *
+ * @since 3.0
+ */
+public class JacobiPreconditioner extends RealLinearOperator {
+
+    /** The diagonal coefficients of the preconditioner. */
+    private final ArrayRealVector diag;
+
+    /**
+     * Creates a new instance of this class.
+     *
+     * @param diag the diagonal coefficients of the linear operator to be preconditioned
+     * @param deep {@code true} if a deep copy of the above array should be performed
+     */
+    public JacobiPreconditioner(final double[] diag, final boolean deep) {
+        this.diag = new ArrayRealVector(diag, deep);
+    }
+
+    /**
+     * Creates a new instance of this class. This method extracts the diagonal coefficients of the
+     * specified linear operator. If {@code a} does not extend {@link AbstractRealMatrix}, then the
+     * coefficients of the underlying matrix are not accessible, coefficient extraction is made by
+     * matrix-vector products with the basis vectors (and might therefore take some time). With
+     * matrices, direct entry access is carried out.
+     *
+     * @param a the linear operator for which the preconditioner should be built
+     * @return the diagonal preconditioner made of the inverse of the diagonal coefficients of the
+     *     specified linear operator
+     * @throws NonSquareOperatorException if {@code a} is not square
+     */
+    public static JacobiPreconditioner create(final RealLinearOperator a)
+            throws NonSquareOperatorException {
+        final int n = a.getColumnDimension();
+        if (a.getRowDimension() != n) {
+            throw new NonSquareOperatorException(a.getRowDimension(), n);
+        }
+        final double[] diag = new double[n];
+        if (a instanceof AbstractRealMatrix) {
+            final AbstractRealMatrix m = (AbstractRealMatrix) a;
+            for (int i = 0; i < n; i++) {
+                diag[i] = m.getEntry(i, i);
+            }
+        } else {
+            final ArrayRealVector x = new ArrayRealVector(n);
+            for (int i = 0; i < n; i++) {
+                x.set(0.);
+                x.setEntry(i, 1.);
+                diag[i] = a.operate(x).getEntry(i);
+            }
+        }
+        return new JacobiPreconditioner(diag, false);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public int getColumnDimension() {
+        return diag.getDimension();
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public int getRowDimension() {
+        return diag.getDimension();
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public RealVector operate(final RealVector x) {
+        // Dimension check is carried out by ebeDivide
+        return new ArrayRealVector(MathArrays.ebeDivide(x.toArray(), diag.toArray()), false);
+    }
+
+    /**
+     * Returns the square root of {@code this} diagonal operator. More precisely, this method
+     * returns P = diag(1 / &radic;A<sub>11</sub>, 1 / &radic;A<sub>22</sub>, &hellip;).
+     *
+     * @return the square root of {@code this} preconditioner
+     * @since 3.1
+     */
+    public RealLinearOperator sqrt() {
+        final RealVector sqrtDiag = diag.map(new Sqrt());
+        return new RealLinearOperator() {
+            /** {@inheritDoc} */
+            @Override
+            public RealVector operate(final RealVector x) {
+                return new ArrayRealVector(
+                        MathArrays.ebeDivide(x.toArray(), sqrtDiag.toArray()), false);
+            }
+
+            /** {@inheritDoc} */
+            @Override
+            public int getRowDimension() {
+                return sqrtDiag.getDimension();
+            }
+
+            /** {@inheritDoc} */
+            @Override
+            public int getColumnDimension() {
+                return sqrtDiag.getDimension();
+            }
+        };
+    }
+}