Data update

Task/Steffensens-method/JavaScript/steffensens-method.js

@@ -0,0 +1,69 @@
+class Steffensen {
+    static aitken(p0) {
+        const p1 = this.f(p0);
+        const p2 = this.f(p1);
+        const p1m0 = p1 - p0;
+        return p0 - p1m0 * p1m0 / (p2 - 2.0 * p1 + p0);
+    }
+
+    static steffensenAitken(pinit, tol, maxiter) {
+        let p0 = pinit;
+        let p = this.aitken(p0);
+        let iter = 1;
+        while (Math.abs(p - p0) > tol && iter < maxiter) {
+            p0 = p;
+            p = this.aitken(p0);
+            iter++;
+        }
+        if (Math.abs(p - p0) > tol) return null;
+        return p;
+    }
+
+    static deCasteljau(c0, c1, c2, t) {
+        const s = 1.0 - t;
+        const c01 = s * c0 + t * c1;
+        const c12 = s * c1 + t * c2;
+        return s * c01 + t * c12;
+    }
+
+    static xConvexLeftParabola(t) {
+        return this.deCasteljau(2.0, -8.0, 2.0, t);
+    }
+
+    static yConvexRightParabola(t) {
+        return this.deCasteljau(1.0, 2.0, 3.0, t);
+    }
+
+    static implicitEquation(x, y) {
+        return 5.0 * x * x + y - 5.0;
+    }
+
+    static f(t) {
+        const x = this.xConvexLeftParabola(t);
+        const y = this.yConvexRightParabola(t);
+        return this.implicitEquation(x, y) + t;
+    }
+
+    static main() {
+        let t0 = 0.0;
+        for (let i = 0; i < 11; ++i) {
+            process.stdout.write(`t0 = ${t0.toFixed(1)} : `);
+            const t = this.steffensenAitken(t0, 0.00000001, 1000);
+            if (t === null) {
+                console.log("no answer");
+            } else {
+                const x = this.xConvexLeftParabola(t);
+                const y = this.yConvexRightParabola(t);
+                if (Math.abs(this.implicitEquation(x, y)) <= 0.000001) {
+                    console.log(`intersection at (${x}, ${y})`);
+                } else {
+                    console.log("spurious solution");
+                }
+            }
+            t0 += 0.1;
+        }
+    }
+}
+
+// Run the main function
+Steffensen.main();